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authorwillemw122018-10-08 10:17:59 +0200
committerwillemw122018-10-08 10:17:59 +0200
commitb4b741d41ba520516ccc8c5151ce0d65a1e5c355 (patch)
treea48294ec28c736cb090573f069198c9b284a3c83
parenta5ffd24ab7c90e423e09524299ecb380309db520 (diff)
downloadaur-b4b741d41ba520516ccc8c5151ce0d65a1e5c355.tar.gz
Update to 4.0.1 and to python3...
Fix createdocs.py HTML manual generation. Add libxslt dependency. Remove .install file and desktop-file-utils dependency. Update "need a graphical environment" comment.
-rw-r--r--.SRCINFO24
-rw-r--r--PKGBUILD54
-rw-r--r--gnofract4d-manual.html1825
-rw-r--r--gnofract4d.install12
4 files changed, 29 insertions, 1886 deletions
diff --git a/.SRCINFO b/.SRCINFO
index c6170faba69..97348f1c0dd 100644
--- a/.SRCINFO
+++ b/.SRCINFO
@@ -1,23 +1,19 @@
-# Generated by mksrcinfo v7
-# Sat Oct 3 07:43:37 UTC 2015
pkgbase = gnofract4d
- pkgdesc = Create beautiful fractal images in PyGTK
- pkgver = 3.14.1
- pkgrel = 4
- url = http://gnofract4d.sourceforge.net
- install = gnofract4d.install
+ pkgdesc = Create beautiful fractal images
+ pkgver = 4.0.1
+ pkgrel = 1
+ url = https://edyoung.github.io/gnofract4d/
arch = any
license = BSD
makedepends = docbook-xsl
- makedepends = python2
- depends = desktop-file-utils
+ makedepends = libxslt
+ depends = gtk3
depends = libjpeg
depends = libpng
- depends = pygtk
- source = https://github.com/edyoung/gnofract4d/archive/V_3_14_1.tar.gz
- source = gnofract4d-manual.html
- md5sums = 0872b6acefa9123205e099c9e174a791
- md5sums = 784e9aeb0abcf473d338481f37503ab0
+ depends = python-cairo
+ depends = python-gobject
+ source = https://github.com/edyoung/gnofract4d/archive/v4.0.1.tar.gz
+ md5sums = 29da10ba5a2747349bae420de956db5b
pkgname = gnofract4d
diff --git a/PKGBUILD b/PKGBUILD
index e35662e44b0..9ae80fa00fa 100644
--- a/PKGBUILD
+++ b/PKGBUILD
@@ -4,57 +4,41 @@
# Contributor: Thomas Dziedzic <gostrc@gmail.com>
# Contributor: Angelo Theodorou <encelo@users.sourceforge.net>
-
-# Note: This build process needs to be run in a graphical environment (createdocs.py and test.py)
-
-
pkgname=gnofract4d
-pkgver=3.14.1
-_pkgver="V_${pkgver//./_}"
-pkgrel=4
-pkgdesc="Create beautiful fractal images in PyGTK"
+pkgver=4.0.1
+pkgrel=1
+pkgdesc="Create beautiful fractal images"
arch=('any')
-url="http://gnofract4d.sourceforge.net"
+url="https://edyoung.github.io/gnofract4d/"
license=('BSD')
-makedepends=('docbook-xsl' 'python2')
-depends=('desktop-file-utils' 'libjpeg' 'libpng' 'pygtk')
-install=$pkgname.install
-source=(https://github.com/edyoung/gnofract4d/archive/$_pkgver.tar.gz
- gnofract4d-manual.html)
-md5sums=('0872b6acefa9123205e099c9e174a791'
- '784e9aeb0abcf473d338481f37503ab0')
+makedepends=('docbook-xsl' 'libxslt')
+depends=('gtk3' 'libjpeg' 'libpng' 'python-cairo' 'python-gobject')
+source=(https://github.com/edyoung/gnofract4d/archive/v$pkgver.tar.gz)
+md5sums=('29da10ba5a2747349bae420de956db5b')
prepare() {
- cd $pkgname-$_pkgver
-
+ cd $pkgname-$pkgver
+ # Patch for createdocs.py
sed -i "s|/usr/share/sgml/docbook/stylesheet/xsl/nwalsh/xhtml/docbook.xsl|/usr/share/xml/docbook/xsl-stylesheets-"$(pacman -Q docbook-xsl | \
- awk '{ print $2 }' | awk -F"-" '{ print $1 }')"/manpages/docbook.xsl|" \
+ awk '{ print $2 }' | awk -F"-" '{ print $1 }')"/xhtml/docbook.xsl|" \
doc/gnofract4d-manual/C/gnofract4d.xsl
-
- # For running tests in check()
- #find . -name "*.py" -exec sed -i "s|env python|env python2|" '{}' \;
- #find . -name "*.py" -exec sed -i "s|/usr/bin/python|/usr/bin/python2|" '{}' \;
}
build() {
- cd $pkgname-$_pkgver
- python2 setup.py build
- python2 createdocs.py
+ cd $pkgname-$pkgver
+ ./setup.py build
+ ./createdocs.py
}
+# Note: the tests need to be run in a graphical environment
#check() {
-# cd $pkgname-$_pkgver
-# python2 test.py
+# cd $pkgname-$pkgver
+# ./test.py
#}
package() {
- cd $pkgname-$_pkgver
- python2 setup.py install --root="$pkgdir" --optimize=1
- install -Dm644 COPYING "$pkgdir/usr/share/licenses/$pkgname/COPYING"
+ cd $pkgname-$pkgver
install -Dm644 doc/gnofract4d.1 "$pkgdir/usr/share/man/man1/$pkgname.1"
-
- # Patch for createdocs.py. Generating "Formula Reference Reference" entries fails:
- # Error: no refentry: No refentry elements found in "Gnofract 4D". Gnofract 4D
- install -m644 "$srcdir/gnofract4d-manual.html" "$pkgdir/usr/share/gnome/help/gnofract4d/C/gnofract4d-manual.html"
+ ./setup.py install --root="$pkgdir" --optimize=1
}
diff --git a/gnofract4d-manual.html b/gnofract4d-manual.html
deleted file mode 100644
index 07706d7e5d6..00000000000
--- a/gnofract4d-manual.html
+++ /dev/null
@@ -1,1825 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Gnofract 4D</title><link rel="stylesheet" href="docbook.css" type="text/css" /><meta name="generator" content="DocBook XSL Stylesheets V1.75.2" /></head><body><div class="article" title="Gnofract 4D"><div class="titlepage"><div><div><h2 class="title"><a id="gnofract4d"></a>Gnofract 4D</h2></div><div><h3 class="subtitle"><i><span class="emphasis"><em>For when 2D fractals just aren't weird enough</em></span></i></h3></div><div><div class="author"><h3 class="author"><span class="firstname">Tim</span> <span class="surname">Whidbey</span></h3></div></div></div><hr /></div><div class="toc"><p><b>Table of Contents</b></p><dl><dt><span class="sect1"><a href="#introduction">Introduction</a></span></dt><dt><span class="sect1"><a href="#using">Using <span class="application">Gnofract 4D</span></a></span></dt><dd><dl><dt><span class="sect2"><a href="#basics">Interacting with the Fractal</a></span></dt><dt><span class="sect2"><a href="#files">Working with Files</a></span></dt><dt><span class="sect2"><a href="#tools">Tools</a></span></dt><dt><span class="sect2"><a href="#toolbar">Toolbar buttons</a></span></dt><dt><span class="sect2"><a href="#preferences">Changing Fractal Settings</a></span></dt><dt><span class="sect2"><a href="#hints">Hints</a></span></dt></dl></dd><dt><span class="sect1"><a href="#cmdref">Command Reference</a></span></dt><dd><dl><dt><span class="sect2"><a href="#MouseCommands">Mouse Commands</a></span></dt><dt><span class="sect2"><a href="#KeyboardShortcuts">Keyboard Shortcuts</a></span></dt></dl></dd><dt><span class="sect1"><a href="#maths"> About the maths</a></span></dt><dd><dl><dt><span class="sect2"><a href="#mset">The Mandelbrot Set</a></span></dt><dt><span class="sect2"><a href="#julia">The Julia Set</a></span></dt><dt><span class="sect2"><a href="#julibrot">The Julibrot</a></span></dt><dt><span class="sect2"><a href="#viewing">Viewing in Four Dimensions</a></span></dt><dt><span class="sect2"><a href="#hypercomplex">Hypercomplex Fractals and Quaternions</a></span></dt></dl></dd><dt><span class="sect1"><a href="#compiler">Writing Your Own Functions</a></span></dt><dd><dl><dt><span class="sect2"><a href="#frm_tutorial">Writing Your First Formula</a></span></dt></dl></dd><dt><span class="sect1"><a href="#formref">Formula Language Reference</a></span></dt><dd><dl><dt><span class="sect2"><a href="#Operators">Operators</a></span></dt><dt><span class="sect2"><a href="#Functions">Functions</a></span></dt><dt><span class="sect2"><a href="#Symbols">Symbols</a></span></dt></dl></dd><dt><span class="sect1"><a href="#internals"><span class="application">Gnofract 4D</span> Internals</a></span></dt><dd><dl><dt><span class="sect2"><a href="#layout">Source Code Layout</a></span></dt><dt><span class="sect2"><a href="#compiler_internals">Compiler</a></span></dt><dt><span class="sect2"><a href="#threading">Threading</a></span></dt></dl></dd><dt><span class="sect1"><a href="#bugs">Bugs and Known Issues</a></span></dt><dd><dl><dt><span class="sect2"><a href="#reporting">Reporting Bugs</a></span></dt><dt><span class="sect2"><a href="#compat">Backwards Compatibility</a></span></dt></dl></dd><dt><span class="sect1"><a href="#about">About <span class="application">Gnofract 4D</span></a></span></dt><dd><dl><dt><span class="sect2"><a href="#credits">Credits and copyright</a></span></dt></dl></dd></dl></div><div class="sect1" title="Introduction"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="introduction"></a>Introduction</h2></div></div></div><div class="epigraph"><p>
-There is no excellent beauty which hath not some strangeness in the
-proportion.</p><div class="attribution"><span>—<span class="attribution">Francis Bacon</span></span></div></div><p><span class="application">Gnofract 4D</span> is a program which draws complex mathematical
-objects known as fractals, including the Mandelbrot and Julia sets and
-many others. It allows you to treat a fractal which has more than one
-parameter as a four-dimensional object and interactively view slices
-of this object from arbitrary angles, giving rise to some very unusual
-images.
-</p><p>
-This user's manual provides a tutorial introduction to <span class="application">Gnofract 4D</span> and the
-mathematical background behind it, information on how to use the
-graphical interface, and reference material on the language used to
-write fractal formulas.
-
-</p></div><div class="sect1" title="Using Gnofract 4D"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="using"></a>Using <span class="application">Gnofract 4D</span></h2></div></div></div><p>
-
-<span class="application">Gnofract 4D</span>'s screen layout is deliberately simple. Most of the screen is
-taken up by a viewport onto the fractal you're investigating. By
-default, this is the Mandelbrot set. You can directly click on this to
-zoom. The toolbar provides quick access to frequently used functions,
-and more complex properties of the fractal are accessed through dialog
-boxes brought up via the menu bar.
-</p><p>
-Initially, just play around - after all, generating fractals isn't
-meant to be <span class="emphasis"><em>work</em></span>. If you make a change you don't
-like, just hit Undo.
-</p><div class="sect2" title="Interacting with the Fractal"><div class="titlepage"><div><div><h3 class="title"><a id="basics"></a>Interacting with the Fractal</h3></div></div></div><p>
-Each fractal is an infinitely complex image, which you can see a slice
-of in the main window. By left-clicking on the window, you can zoom in
-to view finer and finer details. Just click on an area you like to
-view it more closely. If you click and drag with the left button, you can
-draw a white box around an area. When you let go, you zoom in
-so that the area inside that box fills the window.
-</p><p>
-To zoom back out, click with the right button. You can also press
-<span class="keycap"><strong>Home</strong></span> to return all parameters to the starting point
-for this fractal, <span class="keycap"><strong>Control</strong></span>+<span class="keycap"><strong>Home</strong></span> to
-reset the zoom only, or use <span class="guibutton">Undo</span> to go back one
-step. There isn't a click and drag feature for the right button.
-</p><p>
-Clicking with the middle button rotates the view by 90 degrees in the
-<span class="emphasis"><em>xz</em></span> and <span class="emphasis"><em>yw</em></span> axes. If you're
-currently looking at the Mandelbrot set, you'll get a Julia set, and
-vice versa. If you're looking at something else, you'll get something
-weird. Note that clicking this twice doesn't take you back to where
-you started: the screen also gets recentered on the point you clicked,
-so clicking twice will normally give you a perturbed, deformed-looking
-Mandelbrot.
-</p><p>
-The cursor keys pan around the image. Hold down
-<span class="keycap"><strong>Control</strong></span>+ <span class="keycap"><strong>&lt;cursor&gt;</strong></span> to move more
-quickly. Hold down <span class="keycap"><strong>Shift</strong></span> +
-<span class="keycap"><strong>&lt;cursor&gt;</strong></span> to move around in the other two
-dimensions, mutating the image. You can recenter the image on a point
-by left-clicking on that point while holding down
-<span class="keycap"><strong>Shift</strong></span>. </p><div class="note" title="Non-4D formulas" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Non-4D formulas</h3><p> Some fractal formulas
-(typically those originally written for Fractint or UltraFractal)
-don't support full 4D operation. (<span class="application">Gnofract 4D</span> determines this by whether
-the formula uses the <code class="varname">#zwpixel</code> variable.) In this
-case, the widgets for rotating in other dimensions, warping, and the
-middle mouse button will be disabled. </p></div></div><div class="sect2" title="Working with Files"><div class="titlepage"><div><div><h3 class="title"><a id="files"></a>Working with Files</h3></div></div></div><p>
-
-<span class="application">Gnofract 4D</span> uses several different types of file. These have different
-purposes as listed in the table below.
-
-</p><div class="informaltable"><table border="1"><colgroup><col /><col /><col /></colgroup><thead><tr><th>File Type</th><th>Extensions</th><th>Description</th></tr></thead><tbody><tr><td>
-Parameter File
-</td><td><code class="filename">.fct</code></td><td>
-
-A parameter file is a small text file which contains all the settings
-required to produce a particular image, such as the position of the
-viewer along the X axis and the coloring scheme used. The parameter
-file lists the formula used, but doesn't contain the entire formula,
-so if you invent a new formula and want to share parameter files which
-use it, you need to distribute the formula file as well.
-
-<span class="application">Fractint</span> uses <code class="filename">.par</code> files for
-this purpose and <span class="application">UltraFractal</span> uses <code class="filename">.upr</code>.
-Unfortunately <span class="application">Gnofract 4D</span> can't read
-those formats (yet).
-</td></tr><tr><td>
-Image File
-</td><td>
-<code class="filename">.jpg</code>,
-<code class="filename">.png</code>
-</td><td>
-<span class="application">Gnofract 4D</span> supports JPEG and PNG file formats for image
-output. <span class="emphasis"><em>No information about the fractal parameters is
-stored in the image file</em></span>, so if you want to carry on
-exploring from a particular point you need to save a parameter file as
-well. <span class="application">Gnofract 4D</span> can't load image files, only save them. Choose
-<span class="guimenu">File</span> &gt; <span xmlns="" class="guimenuitem"><span xmlns="http://www.w3.org/1999/xhtml" class="guimenuitem">Save Image</span></span> to
-save an image.
-I recommend
-using PNG images for high quality output, and JPEGs only when image
-size is important, because JPEGs introduce artifacts which blur the
-fine details of your fractal.
-</td></tr><tr><td>
-Formula File
-</td><td>
-<code class="filename">.frm</code>,
-<code class="filename">.ufm</code>
-</td><td>
-
-A formula file is a collection of formulas, each of which is a
-description of the algorithm used to draw a particular kind of
-fractal, expressed in a simple programming language (see <a class="xref" href="#formref" title="Formula Language Reference">the section called “Formula Language Reference”</a> for language details). Both <span class="application">Gnofract 4D</span> and <span class="application">Fractint</span>
-use <code class="filename">.frm</code> as the extension, and
-<span class="application">UltraFractal</span> uses <code class="filename">.ufm</code>. In
-general, any formula which works in <span class="application">Fractint</span> should work in <span class="application">Gnofract 4D</span>
-and any which works in <span class="application">Gnofract 4D</span> should work in <span class="application">UltraFractal</span>, but the
-reverse is not true.
-
-</td></tr><tr><td>
-Coloring Algorithm File
-</td><td>
-<code class="filename">.cfrm</code>,
-<code class="filename">.ucl</code>
-</td><td>
-
-A coloring algorithm file is a collection of formulas used to assign
-colors to a fractal. <span class="application">Gnofract 4D</span> combines a coloring algorithm with a
-formula to produce the final image (this approach is shared with
-<span class="application">UltraFractal</span> - <span class="application">Fractint</span> restricts you to built-in coloring
-algorithms). Coloring algorithms are written in the same language as
-fractal formulas. <span class="application">UltraFractal</span> uses the extension .ucl for its
-coloring algorithm files. Some of these are compatible with <span class="application">Gnofract 4D</span> but
-so far not very many.
-</td></tr><tr><td>
-Gradient File
-</td><td>
-<code class="filename">.map</code>,
-<code class="filename">.ggr</code>
-<code class="filename">.ugr</code>
-</td><td>
-
-A gradient file is a list of colors which is used to translate the
-purely numerical output of the formula into something pretty to look
-at. Gradients are currently saved only inside the fractal itself, not
-as separate files. The GIMP uses the extension .ggr for its gradient
-files; <span class="application">Fractint</span> uses .map for its own, simpler files. <span class="application">UltraFractal</span>
-uses .ugr - these files contain multiple gradients.
-
-</td></tr></tbody></table></div><p>
-</p></div><div class="sect2" title="Tools"><div class="titlepage"><div><div><h3 class="title"><a id="tools"></a>Tools</h3></div></div></div><div class="sect3" title="Autozoom"><div class="titlepage"><div><div><h4 class="title"><a id="autozoom"></a>Autozoom</h4></div></div></div><p> Autozoom automatically searches for interesting parts of the
-fractal by zooming in repeatedly, each time choosing the quadrant of
-the screen which has the largest number of different colors (with some
-randomization as well). You can start it going, go off for a coffee,
-and see what it's found when you return, or guide it by clicking on
-parts you like as it goes. It'll stop when the image reaches the
-minimum size, which is set by default to stop just before you get to
-the limits of the precision <span class="application">Gnofract 4D</span> offers.
-</p></div><div class="sect3" title="Explorer"><div class="titlepage"><div><div><h4 class="title"><a id="explorer"></a>Explorer</h4></div></div></div><p>
-The <span class="emphasis"><em>Explorer</em></span> helps you find neat-looking fractals
-easily. It divides the screen into a large central section and smaller
-"subfractals" which surround it. The central section is the main image
-- you can click on this to zoom in, change the color, or perform any
-operation you can normally. The other images around the edges are
-"mutant" versions of the main image - they're formed by starting with
-the base parameters and randomly changing them a bit. Whenever you
-change the main image, you get a whole new set of mutants. If you like
-a mutant more than the main picture, click on it to move it to the
-middle - it then becomes the main picture and you get 12 new mutants
-based on the new main image. When you're satisfied with the results,
-click the Explorer button again to return to normal mode. </p><p> The Shape and Color sliders on the toolbar determines how
-different the mutants are from the standard image. If Shape's set to
-100, they're almost unrecognizable - if it's 0, they're exactly the
-same. Similarly if Color's 100, each mutant is a different color, and
-0 keeps the colors all the same. </p></div><div class="sect3" title="Formula Browser"><div class="titlepage"><div><div><h4 class="title"><a id="browser"></a>Formula Browser</h4></div></div></div><p>
-
-The <span class="emphasis"><em>Formula Browser</em></span> allows you to look at all the
-fractal formulas, coloring functions and gradients which are currently loaded
-formula files. When you select a formula (from the Formula list in the
-middle), the source window shows you the contents of that formula. You
-can then use <span class="guibutton">Apply</span> to change the current
-fractal to use that formula. This also resets the formula's parameters
-to their defaults. Alternatively, <span class="guibutton">OK</span> applies
-the formula and closes the window. </p><p>
-Tips:
-</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"><p> To load a new formula file, choose <span class="guimenu">File</span>
-&gt; <span xmlns="" class="guimenuitem"><span xmlns="http://www.w3.org/1999/xhtml" class="guimenuitem">Open Formula File</span></span>. </p></li><li class="listitem"><p> If you have changed a formula on disk, choose
-<span class="guibutton">Refresh</span> to have <span class="application">Gnofract 4D</span> re-read
-it. </p></li><li class="listitem"><p> If the formula contains errors,
-<span class="guibutton">Apply</span> and <span class="guibutton">OK</span> will be
-disabled. Check the Messages window to see what the errors
-are. </p></li></ul></div><p>
-</p></div><div class="sect3" title="Director"><div class="titlepage"><div><div><h4 class="title"><a id="director"></a>Director</h4></div></div></div><p>
-
-The <span class="emphasis"><em>Director</em></span> allows you to create fractal movies.
-You first define keyframes (including base keyframes) which are stops
-in video. Then, for each of them, you define for how long they last
-(<span class="guilabel">duration</span> - in frames), how long still image of
-keyframe will stay in video (<span class="guilabel">stopped for</span>) and
-interpolation type between several possibilities. When you hit
-<span class="guibutton">Render</span> button, Director will render all frames
-and put them in directory you selected and then it will try to create
-video using <a class="ulink" href="http://www.transcoding.org/" target="_top"><span class="emphasis"><em>transcode</em></span></a>
-tool. </p><p>
-Tips:
-</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"><p>
-In order to end up with video file, not just a bunch of images, you need to have
-<span class="emphasis"><em>transcode</em></span> tool compiled with support for ImageMagick.
-</p></li><li class="listitem"><p>
-You can always save your animation configuration for later use.
-</p></li><li class="listitem"><p>
-You can always stop rendering images. As long as you use same animation setting again
-(for example, saving them before starting rendering), Director will starts from where
-it stopped last time.
-</p></li></ul></div><p>
-</p></div><div class="sect3" title="Randomize Colors"><div class="titlepage"><div><div><h4 class="title"><a id="randomizecolors"></a>Randomize Colors</h4></div></div></div><p>
-Replaces the current gradient with a randomly-generated new one.
-</p></div><div class="sect3" title="Painter"><div class="titlepage"><div><div><h4 class="title"><a id="painter"></a>Painter</h4></div></div></div><p>
-
-The painter dialog allows you to change the colors of your fractal by
-clicking on the place where you want the color to be different. First,
-select the color you want in the color selector. Then click on the
-image - the part of the gradient most responsible for the color of
-that pixel will be updated with the color you chose. Toggle the
-"painting" button off if you want to interact with the fractal while
-the painter dialog is up.
-
-</p></div></div><div class="sect2" title="Toolbar buttons"><div class="titlepage"><div><div><h3 class="title"><a id="toolbar"></a>Toolbar buttons</h3></div></div></div><p>
-On the left of the toolbar you can see a small preview window, which
-updates as you change the angle or position buttons, to give you an
-idea of what the fractal will look like when you release the button.
-</p><p>
-The first eight toolbar buttons correspond to the ten parameters which
-define the view. The circular angle buttons, labelled
-<span class="emphasis"><em>xy</em></span> to <span class="emphasis"><em>zw</em></span>, correspond to
-rotation around the principal planes in four dimensions. They can
-changed by dragging the dot around. When you let go, the fractal will
-update. By the way, the <span class="emphasis"><em>zw</em></span> angle does work, you
-just can't see its effects until you rotate in some other dimensions
-first. </p><p>
-The square position buttons, <span class="emphasis"><em>pan</em></span> and
-<span class="emphasis"><em>wrp</em></span> (aka Warp), can be used to alter the view. The
-<span class="emphasis"><em>pan</em></span> button allows you to pan around the current
-view. The <span class="emphasis"><em>wrp</em></span> button allows you to move along the
-other two axes, resulting in a mutated version of the current image.
-Click inside one then drag the mouse, watching the preview window
-update, then release the mouse when you like the results. </p><p>The warp menu allows even formulas which weren't designed to be
-used with <span class="application">Gnofract 4D</span> to be used in 4D mode. If the current fractal has any
-complex parameters, they're listed in this menu. If you select one,
-that parameter's value is set to the value of the Z and W coordinates
-for each pixel. Basically what this means is that the parameter you choose
-becomes the fourth dimension. NB: If you set an explicit value for the parameter as
-well, it'll be ignored.
-</p><p>
-The <span class="emphasis"><em>Deepen</em></span> button allows you to increase the current iteration count
-and tighten the periodicity checking, for those occasions when the
-auto-deepening and/or auto-tolerance doesn't get it right. This will
-generally convert some 'inside' pixels to outside and make the image
-look better, at the cost of longer rendering time. The image size list should be
-self-explanatory. If you want a size not listed here, use the
-Preferences dialog. </p><p> The <span class="emphasis"><em>Undo</em></span> and
-<span class="emphasis"><em>Redo</em></span> buttons should be fairly obvious. You can
-undo as many times as you like. Note that undo also affects parameters
-such as color, not just position on screen. Lastly, the
-<span class="emphasis"><em>Explore</em></span> button toggles Explorer Mode. See <a class="xref" href="#explorer" title="Explorer">the section called “Explorer”</a>.</p></div><div class="sect2" title="Changing Fractal Settings"><div class="titlepage"><div><div><h3 class="title"><a id="preferences"></a>Changing Fractal Settings</h3></div></div></div><p> In <span class="application">Gnofract 4D</span>, settings are divided into <span class="emphasis"><em>Fractal
-Settings</em></span>, <span class="emphasis"><em>Gradients</em></span> and
-<span class="emphasis"><em>Preferences</em></span>. <span class="emphasis"><em>Fractal
-Settings</em></span> and <span class="emphasis"><em>Gradients</em></span> are saved in the
-fractal's .fct file - they are properties of the fractal itself. By
-contrast, <span class="emphasis"><em> Preferences</em></span> are your preferences for
-<span class="application">Gnofract 4D</span>'s general behavior and are saved in <span class="application">Gnofract 4D</span>'s config file
-(~/.gnofract4d), so they will still be active next time you
-start <span class="application">Gnofract 4D</span> </p><div class="sect3" title="Fractal Settings"><div class="titlepage"><div><div><h4 class="title"><a id="settingsdialog"></a>Fractal Settings</h4></div></div></div><p>
-
-The <span class="emphasis"><em>Formula</em></span> section allows you to choose the
-formula used to calculate the fractal, and to set any parameters the
-formula has. You can modify the formula by choosing <span class="guibutton">Browse
-</span>, which invokes the Formula Browser. <span class="emphasis"><em>Max
-Iterations</em></span> sets the number of iterations a point will go
-through before we give up and assume it's a member of the
-Julibrot. The other parameters on this pane are different depending on
-the fractal type.
-</p><p>
-The <span class="emphasis"><em>Outer</em></span> page controls the function used to
-decide what color to draw those points which aren't part of the
-fractal set proper. Similarly, the <span class="emphasis"><em>Inner</em></span> page
-controls the function used for points which are part of the set.
-</p><p>
-The <span class="emphasis"><em>Location</em></span> entryboxes allow you to
-change the coordinates of the screen center and the image size.
-
-The <span class="emphasis"><em>Angles</em></span> entryboxes allows you to set the rotation
-angles. Only values between 0 and 2 * pi are different; values outside
-this range "wrap" to points inside that range.
-</p><p>
-
-The <span class="emphasis"><em>Transforms</em></span> page allows you to control a list
-of transformations applied to the image, and any parameters those transforms have.
-</p><p>
-The <span class="emphasis"><em>General</em></span> page gives a few options which don't
-fit anywhere else. <span class="emphasis"><em>Flip Y Axis</em></span> causes Y to
-increase top-to-bottom, rather than
-bottom-to-top. <span class="emphasis"><em>Periodicity Checking</em></span> is a method
-to speed up generation of the fractal. Points inside the fractal
-eventually settle into a loop, where they repeatedly jump around
-between the same points (they become 'periodic'). By noticing this, we
-can skip calculating the point any further. You will generally want to
-disable this if you are coloring the inside of the fractal, since it
-will look rather weird otherwise. <span class="emphasis"><em>Tolerance</em></span> is
-the distance between points which we'll accept as being 'the same' for
-the purposes of periodicity detection. This is automatically adjusted
-if the 'auto tolerance' setting in the preferences is enabled.
-
-</p><p>
-
-The <span class="emphasis"><em>Colors</em></span> tab allows you to edit the list of
-colors used to display your fractal. For more complex gradient
-editing, you can also use the GIMP's gradient editor.
-
-</p></div><div class="sect3" title="Preferences"><div class="titlepage"><div><div><h4 class="title"><a id="prefsdialog"></a>Preferences</h4></div></div></div><div class="sect4" title="Image"><div class="titlepage"><div><div><h5 class="title"><a id="prefs_image"></a>Image</h5></div></div></div><p> <span class="emphasis"><em>Width</em></span> and <span class="emphasis"><em>Height</em></span> set
-the size of the image in pixels. If <span class="emphasis"><em>Maintain Aspect
-Ratio</em></span> is checked when you change either the width or
-height, the other automatically changes to keep the image the same
-shape. If <span class="emphasis"><em>Auto Deepen</em></span> is enabled, <span class="application">Gnofract 4D</span> will try
-to automatically guess how many iterations are required to display the
-image correctly. Similarly, <span class="emphasis"><em>Auto Tolerance</em></span>
-adjusts the periodicity tolerance setting to try and calculate the
-image quickly but correctly. <span class="emphasis"><em>Antialiasing</em></span> makes
-the image look smoother but takes extra time to do. The difference
-between 'fast' and 'best' is that fast antialiasing doesn't bother to
-recalculate points which are the same color as their neighbors. This
-speeds things up a lot but can miss a few details sometimes. </p></div><div class="sect4" title="Compiler"><div class="titlepage"><div><div><h5 class="title"><a id="prefs_compiler"></a>Compiler</h5></div></div></div><p>
-<span class="application">Gnofract 4D</span> needs a C compiler to be available at runtime in order to work
-(it dynamically creates the code to compute a particular formula when
-you select it). The <span class="emphasis"><em>Compiler</em></span> page allows you to
-specify a location for the compiler and options to pass to
-it. <span class="emphasis"><em>If <span class="application">Gnofract 4D</span> is working fine, generally I suggest you leave
-those settings alone. However you <span class="emphasis"><em>may</em></span> be able to
-get noticeable performance gains by specifying the specific kind of
-processor you have. For example, fairly modern AMD processors will
-benefit by adding "-mathlon -msse2 -m3dnow" to the compiler flags.
-
-</em></span> The <span class="emphasis"><em>Formula Search
-Path</em></span> lists the directories where <span class="application">Gnofract 4D</span> will look for
-formulas when a parameter file is loaded.
-</p></div><div class="sect4" title="General"><div class="titlepage"><div><div><h5 class="title"><a id="prefs_general"></a>General</h5></div></div></div><p>
-
-<span class="emphasis"><em>Number of threads</em></span> sets how many calculation
-threads to use. Generally, leave this at 1 unless you have a
-hyper-threaded or multi-processor computer, in which case set it to 1
-greater than the number of CPUs you have.
-</p></div><div class="sect4" title="Helpers"><div class="titlepage"><div><div><h5 class="title"><a id="prefs_helpers"></a>Helpers</h5></div></div></div><p>
-
-<span class="application">Gnofract 4D</span> sometimes need to invoke a helper program. It'll try to use
-your preferences from GConf if possible, and these fields are set to
-be those defaults. However if that default is wrong somehow, you can
-explicitly set it here.
-</p></div><div class="sect4" title="Flickr"><div class="titlepage"><div><div><h5 class="title"><a id="prefs_flickr"></a>Flickr</h5></div></div></div><p>
-
-<span class="application">Gnofract 4D</span> can upload your images to the online image-sharing service
-Flickr. This page handles your online identity.
-
-</p></div></div></div><div class="sect2" title="Hints"><div class="titlepage"><div><div><h3 class="title"><a id="hints"></a>Hints</h3></div></div></div><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"><p>If you zoom into a busy part of the fractal the image can look
-"noisy". You can fix this by making the colors change more slowly - go
-to the "Outer" tab and change the transfer function to 'sqrt' or 'log'
-- or change "Density" to a number between 0 and 1 - a density of 0.1
-makes the colors change 10 times more slowly.
-</p></li><li class="listitem"><p>If you have an Inner coloring method other than zero, you may
-see weird effects unless you disable periodicity checking.
-</p></li></ul></div></div></div><div class="sect1" title="Command Reference"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="cmdref"></a>Command Reference</h2></div></div></div><div class="sect2" title="Mouse Commands"><div class="titlepage"><div><div><h3 class="title"><a id="MouseCommands"></a>Mouse Commands</h3></div></div></div><div class="informaltable"><table border="1"><colgroup><col /><col /></colgroup><thead><tr><th>Button</th><th>Action</th></tr></thead><tbody><tr><td>Left-click</td><td>Zoom in</td></tr><tr><td>Left-click and drag</td><td>Draw rectangle to zoom into.</td></tr><tr><td>Shift-Left-click</td><td>Recenter image on point clicked.</td></tr><tr><td>Middle-click</td><td>Flip to Julia set (or back to Mandelbrot).</td></tr><tr><td>Right-click</td><td>Zoom out.</td></tr><tr><td>Control-Right-click</td><td>Zoom out more quickly.</td></tr></tbody></table></div><p>
-</p></div><div class="sect2" title="Keyboard Shortcuts"><div class="titlepage"><div><div><h3 class="title"><a id="KeyboardShortcuts"></a>Keyboard Shortcuts</h3></div></div></div><div class="informaltable"><table border="1"><colgroup><col /><col /></colgroup><thead><tr><th>Key</th><th>Action</th></tr></thead><tbody><tr><td>(arrow)</td><td>Pan image in indicated direction.</td></tr><tr><td>Ctrl+(arrow)</td><td>Pan more quickly in indicated direction.</td></tr><tr><td>Shift+(arrow)</td><td>Mutate image in Z or W directions.</td></tr><tr><td>Shift+Ctrl+(arrow)</td><td>Mutate more quickly.</td></tr><tr><td>Ctrl+1</td><td>Reset rotation to show the XY (Mandelbrot) plane.</td></tr><tr><td>Ctrl+2</td><td>Reset rotation to show the ZW (Julia) plane.</td></tr><tr><td>Ctrl+3</td><td>Reset rotation to show the XZ (Oblate) plane.</td></tr><tr><td>Ctrl+4</td><td>Reset rotation to show the XW (Parabolic) plane.</td></tr><tr><td>Ctrl+5</td><td>Reset rotation to show the YZ (Elliptic) plane.</td></tr><tr><td>Ctrl+6</td><td>Reset rotation to show the WY (Rectangular) plane.</td></tr><tr><td>Ctrl+A</td><td>Display AutoZoom dialog.</td></tr><tr><td>Ctrl+B</td><td>Display formula browser.</td></tr><tr><td>Ctrl+D</td><td>Display the Director (animation) window.</td></tr><tr><td>Ctrl+E</td><td>Enter (or leave) Explorer mode.</td></tr><tr><td>Escape</td><td>Quit full-screen mode.</td></tr><tr><td>Ctrl+F</td><td>Show fractal settings controls.</td></tr><tr><td>Home</td><td>Reset all numeric parameters to their defaults.</td></tr><tr><td>Ctrl+Home</td><td>Reset zoom to default level.</td></tr><tr><td>Ctrl+I</td><td>Save the current image to a file.</td></tr><tr><td>Ctrl+Shift+I</td><td>Add the current fractal to the render queue.</td></tr><tr><td>Ctrl+M</td><td>Launch an email editor with current image attached.</td></tr><tr><td>Ctrl+R</td><td>Create a new random color scheme.</td></tr><tr><td>Ctrl+Shift+S</td><td>Save the current parameters into a new file.</td></tr><tr><td>Ctrl+U</td><td>Upload the current image to Flickr.com.</td></tr><tr><td>Ctrl+Z</td><td>Undo the last operation.</td></tr><tr><td>Ctrl+Shift+Z</td><td>Redo an operation after undoing it.</td></tr><tr><td>F1</td><td>Show help file contents page.</td></tr><tr><td>F11</td><td>Show main window full-screen.</td></tr></tbody></table></div><p>
-</p></div></div><div class="sect1" title="About the maths"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="maths"></a> About the maths</h2></div></div></div><div class="caution" title="Warning: Dubious mathematics ahead" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Warning: Dubious mathematics ahead</h3><p>I'm not a mathematician. You may find this discussion
-insultingly oversimplified or just plain wrong.
-</p></div><div class="sect2" title="The Mandelbrot Set"><div class="titlepage"><div><div><h3 class="title"><a id="mset"></a>The Mandelbrot Set</h3></div></div></div><p> The Mandelbrot may be
-defined as the set of all complex numbers which, when you
-repeatedly square them and add them again, never become infinite. (The
-official definition of the set is somewhat different: it is the set of
-points in the complex plane whose corresponding Julia sets are
-connected. These end up being the same thing.)
-
-We can tell that a number will eventually reach infinity if it ever
-gets outside a circle of radius 2 around the origin. Unfortunately, we
-can't tell in general that a point will <span class="emphasis"><em>never</em></span>
-become infinite, so we have to estimate by trying a large number of
-times before giving up.
-</p><p>
-In <span class="application">Gnofract 4D</span>, the formula is:
-</p><pre class="programlisting">
-Mandelbrot1 {
-init:
- z = 0
-loop:
- z = z^2 + c
-bailout:
- |z| &lt; 4.0
-}
-</pre><p>
-(|z| means the square of the magnitude of z). We calculate the loop
-function repeatedly until the bailout condition is false or we've
-performed the maximum number of iterations. At that point, if we
-"bailed out", we know we're outside the set: otherwise we're
-(probably) inside.
-</p><p>
-We do this repeatedly for each position on the screen, setting
-<span class="emphasis"><em>c</em></span> to a different value for each point. This gives
-rise to the familiar Mandelbrot set:
-</p><p>
-</p><div align="center"><img src="figures/mandelbrot_standard.png" align="middle" /></div><p>
-</p><p>
-All the points inside the set are (as is traditional) coloured
-black. The points outside the set are different colours depending on
-how long it takes them to escape from the set. These colours aren't
-very mathematically significant, but they look nice.
-</p><p>
-So what happens if <span class="emphasis"><em>z</em></span> is initially set to a
-complex value other than zero? (Strictly speaking, you shouldn't do
-this. Zero is important because it is the <span class="emphasis"><em>critical
-value</em></span> of z^2+c - other values are not mathematically
-meaningful. However, as with most fractal programs, <span class="application">Gnofract 4D</span> allows you
-to draw anything which looks interesting, regardless of its
-mathematical purity.)
-
-Well, you get a rather odd-looking, deformed M-set. This initial
-value, which we'll call <span class="emphasis"><em>z0</em></span>, is called the intial
-perturbation, and sets which have a non-zero <span class="emphasis"><em>z0</em></span>
-are known as <span class="emphasis"><em>perturbed</em></span> sets:
-</p><p>
-</p><div align="center"><img src="figures/mandelbrot_perturbed.png" align="middle" /></div><p>
-
-</p></div><div class="sect2" title="The Julia Set"><div class="titlepage"><div><div><h3 class="title"><a id="julia"></a>The Julia Set</h3></div></div></div><p>
-The Julia set is actually drawn by the same procedure as the
-Mandelbrot set. But instead of changing the value of
-<span class="emphasis"><em>c</em></span> for each pixel, we keep <span class="emphasis"><em>c</em></span>
-constant and change <span class="emphasis"><em>z0</em></span>. There is a different
-Julia set for each value of <span class="emphasis"><em>c</em></span>; here's the one for
-<span class="emphasis"><em>c</em></span>=0.
-</p><p>
-</p><div align="center"><img src="figures/julia_standard.png" align="middle" /></div><p>
-
-</p><p>
-Boring, isn't it? That's because we're just squaring the value at each
-iteration without adding anything to it. So any value which starts
-with a magnitude less than 1 will shrink forever (and hence is a
-member of the set). All other values will grow forever, and so we've
-just discovered a rather inefficient way of drawing perfect circles.
-If we use a different value of <span class="emphasis"><em>c</em></span> we get something more
-interesting:
-</p><p>
-</p><div align="center"><img src="figures/julia_perturbed.png" align="middle" /></div><p>
-
-</p></div><div class="sect2" title="The Julibrot"><div class="titlepage"><div><div><h3 class="title"><a id="julibrot"></a>The Julibrot</h3></div></div></div><p>
-
-Here we come to the heart of the matter. I said above that both the
-Julia and Mandelbrot sets are drawn with the <span class="emphasis"><em>same
-function</em></span>.
-</p><pre class="programlisting">
-julibrot(z0,c) {
-init:
- z = z0
-loop:
- z = z^2 + c
-bailout:
- |z| &lt; 4.0
-}
-</pre><p>
-
-The Julibrot function has two complex parameters, or four real
-ones. In <span class="application">Gnofract 4D</span> I refer to the real parameters as x, y, z, and w:
-these are c.re , c.im, z0.re and z0.im respectively.
-
-The only difference is which points we choose to draw. To draw the
-Mandelbrot set, we keep <span class="emphasis"><em>z0</em></span> constant and change
-<span class="emphasis"><em>c</em></span> with each pixel. To draw the Julia set, we keep
-<span class="emphasis"><em>c</em></span> constant and change <span class="emphasis"><em>z0</em></span>. If
-you squint with your brain a bit, you can imagine both sets as
-orthogonal "slices" through the same four-dimensional object. In
-<span class="application">Gnofract 4D</span> terms, the Mandelbrot set is the <span class="emphasis"><em>xy</em></span>
-plane, and the Julia set is the <span class="emphasis"><em>zw</em></span> plane. We can
-also look at other planes: here's an image of the
-<span class="emphasis"><em>xw</em></span> plane:
-</p><p>
-</p><div align="center"><img src="figures/xw_plane.png" align="middle" /></div><p>
-
-</p></div><div class="sect2" title="Viewing in Four Dimensions"><div class="titlepage"><div><div><h3 class="title"><a id="viewing"></a>Viewing in Four Dimensions</h3></div></div></div><p>
-However, we can draw any 2D slice we like, not just those which are
-parallel to the Julibrot axes. To do this we'll need to describe our
-scene by four things. First, the (<span class="emphasis"><em>x,y,z,w</em></span>)
-coordinates of the center of the screen. Second, a vector for the
-x-axis of the screen. This tells us how to change the parameters to
-the Julibrot function as we proceed across the screen. Third, a vector
-for the y-axis. Fourth and finally, the size of the image. For the
-Mandelbrot set, our "default" view, the screen is centered at
-[0,0,0,0], the x-vector is [1,0,0,0] and the y-vector is
-[0,1,0,0]. The initial size is 4, because the whole Mandelbrot set
-fits inside the 2x2 square. We can zoom into the set by changing
-<span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span> and the zoom factor.
-</p><p>
-If we want to draw other slices, we need to rotate our view through
-four dimensions. In 3D, we can rotate in 3 directions: around the
-<span class="emphasis"><em>x</em></span>, <span class="emphasis"><em>y</em></span>, and
-<span class="emphasis"><em>z</em></span> axes. In 4D, we rotate around a <span class="emphasis"><em>
-plane </em></span> rather than a line, and we can rotate in 6
-directions: around the <span class="emphasis"><em>xy, xz, xw, yz, yw</em></span> and
-<span class="emphasis"><em>zw</em></span> planes. For example, if we rotate through 90
-degrees in the xz and yw directions, our screen vectors become
-[0,0,1,0] and [0,0,0,1]: in other words, the Julia set. If we rotate
-only part of the way, we get a "hybrid" between the two sets, which
-looks decidedly odd:
-</p><p>
-</p><div align="center"><img src="figures/hybrid.png" align="middle" /></div><p>
-</p><p>
-In fact, we can rotate to any angle in each of the planes,
-creating a whole world of bizarre pictures.
-</p></div><div class="sect2" title="Hypercomplex Fractals and Quaternions"><div class="titlepage"><div><div><h3 class="title"><a id="hypercomplex"></a>Hypercomplex Fractals and Quaternions</h3></div></div></div><p> There are other kinds of fractal which are commonly described
-as "four-dimensional" - hypercomplex and quaternion-based
-fractals. Hypercomplex numbers have four components (one real and
-three imaginary) where complex numbers have two. Since the
-hypercomplex mandelbrot has two hypercomplex parameters, in <span class="application">Gnofract 4D</span>
-terms it's actually an eight-dimensional object. <span class="application">Gnofract 4D</span> allows you to
-set four of these as part of the view - the other four have to be set
-via parameters. <span class="application">Gnofract 4D</span> doesn't support quaternions at present.</p></div></div><div class="sect1" title="Writing Your Own Functions"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="compiler"></a>Writing Your Own Functions</h2></div></div></div><p>
-When you get tired of the fractal functions which come with Gnofract
-4D, you can write your own, or take advantage of thousands of formulas
-written by other fractal enthusiasts. Gnofract4D can load most fractal
-formula files written for <span class="application">Fractint</span> (and some written for
-<span class="application">UltraFractal</span>). However the compiler is not 100%
-backwards-compatible with <span class="application">Fractint</span>, so unfortunately some fractals
-can't be loaded, or will display differently when they do. <span class="application">Gnofract 4D</span>
-also supports many constructs <span class="application">Fractint</span> doesn't, so you need to take
-extra care when writing formulas if you want them to work in <span class="application">Fractint</span>
-too.
-</p><p>
-Here are links to some online resources for formula files:
-</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"><p> <a class="ulink" href="http://home.att.net/~Paul.N.Lee/OrgForm.html" target="_top">ORGFORM.ZIP</a>
-A collection of about 25,000 <span class="application">Fractint</span> formula files by many authors,
-originally compiled by George C. Martin and currently maintained by
-Paul N. Lee. Indispensable. </p></li><li class="listitem"><p> <a class="ulink" href="http://formulas.ultrafractal.com/" target="_top"><span class="application">UltraFractal</span> public formula
-database</a> Many thousands of formulas by users of
-<span class="application">UltraFractal</span>. Most of these will work with <span class="application">Gnofract 4D</span>. Let me know of
-any issues, since I aim to improve compatibility further in future
-releases. </p></li></ul></div><p>
-</p><div class="sect2" title="Writing Your First Formula"><div class="titlepage"><div><div><h3 class="title"><a id="frm_tutorial"></a>Writing Your First Formula</h3></div></div></div><p>
-This section steps you through the creation of a new fractal
-formula. By the way, the formulas for each of these steps can also be
-found in the file <code class="filename">formulas/tutorial.frm</code>.
-
-</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>
-Create a new file called '<code class="filename">example.frm</code>' (the
-extension is important - <span class="application">Gnofract 4D</span> uses this to decide whether the file
-is a formula or a coloring function).
-</p></li><li class="listitem"><p>
-Enter the following in <code class="filename">example.frm</code>.
-
-</p><pre class="programlisting"><span><span class="bold"><strong>MyFormula {</strong></span></span><span>
-</span><span><span class="emphasis"><em>; First example formula - this produces a variant on the Mandelbrot set</em></span></span><span>
-</span><span><span class="bold"><strong>init:</strong></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>z</span><span> </span><span>=</span><span> </span><span><code class="literal">0</code></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>c</span><span> </span><span>=</span><span> </span><span>#pixel</span><span>
-</span><span><span class="bold"><strong>loop:</strong></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>z</span><span> </span><span>=</span><span> </span><span>z</span><span>*</span><span>z</span><span>*</span><span>c</span><span> </span><span>+</span><span> </span><span>c</span><span>*</span><span>c</span><span>
-</span><span><span class="bold"><strong>bailout:</strong></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>|</span><span>z</span><span>|</span><span> </span><span>&lt;</span><span> </span><span><code class="literal">4.0</code></span><span>
-</span><span>}</span><span>
-</span><span>
-</span></pre><p>
-
-</p></li><li class="listitem"><p>
-Start <span class="application">Gnofract 4D</span>, choose <span xmlns="" class="guimenuitem"><span xmlns="http://www.w3.org/1999/xhtml" class="guimenuitem">File | Open Formula
-File</span></span>, and open example.frm. You should see MyFormula in
-the list of formulas to choose from. Select it and click Apply. You
-should see an image like this:
-</p><p>
-</p><div><img src="figures/tutorial001.png" /></div><p>
-</p><p>
-A few things to note about the formula. It's divided into named
-sections, marked with a colon: "init", "loop". and "bailout". The
-compiler uses these to supply some of the standard scaffolding for a
-fractal function so you don't have to. The "loop" statement is the
-heart of the formula - this is the statement which is run repeatedly
-and which defines the shape of your fractal.
-</p></li><li class="listitem"><p>
-
-At this point, the widgets for rotating the image in 4D will be
-disabled, because your formula doesn't use any of the 4D
-options. Let's turn those on. Edit your formula so it reads:
-
-</p><pre class="programlisting"><span><span class="bold"><strong>MyFormula {</strong></span></span><span>
-</span><span><span class="emphasis"><em>; Second example - introduce 4D</em></span></span><span>
-</span><span><span class="bold"><strong>init:</strong></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>z</span><span> </span><span>=</span><span> </span><span><span class="bold"><strong>#zwpixel</strong></span></span><span> </span><span><span class="emphasis"><em>; take initial value from 4D position</em></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>c</span><span> </span><span>=</span><span> </span><span>#pixel</span><span>
-</span><span><span class="bold"><strong>loop:</strong></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>z</span><span> </span><span>=</span><span> </span><span>z</span><span>*</span><span>z</span><span>*</span><span>c</span><span> </span><span>+</span><span> </span><span>c</span><span>*</span><span>c</span><span>
-</span><span><span class="bold"><strong>bailout:</strong></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>|</span><span>z</span><span>|</span><span> </span><span>&lt;</span><span> </span><span><code class="literal">4.0</code></span><span>
-</span><span>}</span><span>
-</span><span>
-</span></pre><p>
-
-</p><p>
-Then hit <span class="guibutton">Refresh</span> on the Formula Browser window. You
-should now find that all the options are enabled. This is because the image now depends on all 4 components of the 4D space, via #pixel and #zwpixel.
-</p></li><li class="listitem"><p>
-Next let's add some parameters to our function:
-
-</p><pre class="programlisting"><span><span class="bold"><strong>MyFormula {</strong></span></span><span>
-</span><span><span class="emphasis"><em>; Third example - add a parameter</em></span></span><span>
-</span><span><span class="bold"><strong>init:</strong></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>z</span><span> </span><span>=</span><span> </span><span>#zwpixel</span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>c</span><span> </span><span>=</span><span> </span><span>#pixel</span><span>
-</span><span><span class="bold"><strong>loop:</strong></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>z</span><span> </span><span>=</span><span> </span><span><span class="bold"><strong>@myfunc</strong></span></span><span>(</span><span>z</span><span>*</span><span>z</span><span>*</span><span>c</span><span>)</span><span> </span><span>+</span><span> </span><span><span class="bold"><strong>@factor</strong></span></span><span> </span><span>*</span><span> </span><span>z</span><span> </span><span>+</span><span> </span><span>c</span><span>*</span><span>c</span><span>
-</span><span><span class="bold"><strong>bailout:</strong></span></span><span>
-</span><span> </span><span> </span><span> </span><span> </span><span>|</span><span>z</span><span>|</span><span> </span><span>&lt;</span><span> </span><span><code class="literal">4</code></span><span>
-</span><span><span class="bold"><strong>default:</strong></span></span><span>
-</span><span>param</span><span> </span><span>factor</span><span>
-</span><span> </span><span>default</span><span> </span><span>=</span><span> </span><span>(</span><span><code class="literal">1.0</code></span><span>,</span><span><code class="literal">0.5</code></span><span>)</span><span>
-</span><span>endparam</span><span>
-</span><span>}</span><span>
-</span></pre><p>
-
-</p><p>
-Hit <span class="guibutton">Refresh</span> again, then <span xmlns="" class="guimenuitem"><span xmlns="http://www.w3.org/1999/xhtml" class="guimenuitem">Edit |
-Fractal Settings</span></span> to show the formula settings. You
-should two extra parameters in addition to the standard "Max
-Iterations" option: <span class="emphasis"><em>myfunc</em></span>, with a drop-down list
-of functions, and <span class="emphasis"><em>fac</em></span> (or Factor) with a
-draggable 4-way widget and 2 edit boxes. If you set myfunc to
-<span class="emphasis"><em>sqr</em></span> and set factor to (-1,0.5) you should see:
-</p><p>
-</p><div><img src="figures/tutorial002.png" /></div><p>
-</p><p>
-Parameters like this are a quick way to add more options to your
-fractal. Listing them in the "default" section is optional but
-provides a way to pre-populate your formula with values that work
-well. If you leave the default out <span class="application">Gnofract 4D</span> will use "ident" for
-functions and 0 for numeric ones.
-</p></li></ol></div><p>
-</p></div></div><div class="sect1" title="Formula Language Reference"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="formref"></a>Formula Language Reference</h2></div></div></div><div class="sect2" title="Operators"><div class="titlepage"><div><div><h3 class="title"><a id="Operators"></a>Operators</h3></div></div></div><div class="informaltable"><table border="1"><colgroup><col /><col /><col /><col /></colgroup><thead><tr><th>Name</th><th>Description</th><th>Argument Types</th><th>Return Type</th></tr></thead><tbody><tr><td rowspan="4" align="left" valign="top">
-!=</td><td rowspan="4" align="left" valign="top">
-Inequality operator. Compare two values and return true if
- they are different.
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Bool, Bool
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td rowspan="2" align="left" valign="top">
-%</td><td rowspan="2" align="left" valign="top">
-Modulus operator. Computes the remainder when x is divided by y. Not to be confused with the complex modulus.
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-&amp;&amp;</td><td align="left" valign="top">
-Logical AND.
-</td><td align="left" valign="top">
-Bool, Bool
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td rowspan="6" align="left" valign="top">
-*</td><td rowspan="6" align="left" valign="top">
-Multiplication operator.
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper, Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-Hyper, Float
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-Color, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td rowspan="5" align="left" valign="top">
-+</td><td rowspan="5" align="left" valign="top">
-Adds two numbers together.
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper, Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-Color, Color
-</td><td align="left" valign="top">
-Color</td></tr><tr><td rowspan="5" align="left" valign="top">
--</td><td rowspan="5" align="left" valign="top">
-Subtracts two numbers
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper, Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-Color, Color
-</td><td align="left" valign="top">
-Color</td></tr><tr><td rowspan="5" align="left" valign="top">
-/</td><td rowspan="5" align="left" valign="top">
-Division operator
-</td><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex, Float
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper, Float
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-Color, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td rowspan="3" align="left" valign="top">
-&lt;</td><td rowspan="3" align="left" valign="top">
-Less-than operator. Compare two values and return true if the first is less than the second.
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td rowspan="3" align="left" valign="top">
-&lt;=</td><td rowspan="3" align="left" valign="top">
-Less-than-or-equal operator. Compare two values and return true if the first is less than or equal to the second.
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td rowspan="4" align="left" valign="top">
-==</td><td rowspan="4" align="left" valign="top">
-Equality operator. Compare two values and return true if they are
- the same.
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Bool, Bool
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td rowspan="3" align="left" valign="top">
-&gt;</td><td rowspan="3" align="left" valign="top">
-Greater-than operator. Compare two values and return true if the first is greater than the second.
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td rowspan="3" align="left" valign="top">
-&gt;=</td><td rowspan="3" align="left" valign="top">
-Greater-than-or-equal operator. Compare two values and return true if the first is greater than or equal to the second.
-</td><td align="left" valign="top">
-Int, Int
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td rowspan="3" align="left" valign="top">
-^</td><td rowspan="3" align="left" valign="top">
-Exponentiation operator. Computes x to the power y.
-</td><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex, Float
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-not</td><td align="left" valign="top">
-Logical NOT.
-</td><td align="left" valign="top">
-Bool
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-||</td><td align="left" valign="top">
-Logical OR.
-</td><td align="left" valign="top">
-Bool, Bool
-</td><td align="left" valign="top">
-Bool</td></tr></tbody></table></div></div><div class="sect2" title="Functions"><div class="titlepage"><div><div><h3 class="title"><a id="Functions"></a>Functions</h3></div></div></div><div class="informaltable"><table border="1"><colgroup><col /><col /><col /><col /></colgroup><thead><tr><th>Name</th><th>Description</th><th>Argument Types</th><th>Return Type</th></tr></thead><tbody><tr><td align="left" valign="top">
-#rand</td><td align="left" valign="top">
-Each time this is accessed, it returns a new pseudo-random complex number. This is primarily for backwards compatibility with Fractint formulas - use the random() function in new formulas.
-</td><td align="left" valign="top">
-
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-#random</td><td align="left" valign="top">
-Each time this is accessed, it returns a new pseudo-random complex number. This is primarily for backwards compatibility with Fractint formulas - use the random() function in new formulas.
-</td><td align="left" valign="top">
-
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-@fn1</td><td align="left" valign="top">
-Predefined function parameter used by Fractint formulas
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-@fn2</td><td align="left" valign="top">
-Predefined function parameter used by Fractint formulas
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-@fn3</td><td align="left" valign="top">
-Predefined function parameter used by Fractint formulas
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-@fn4</td><td align="left" valign="top">
-Predefined function parameter used by Fractint formulas
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td rowspan="3" align="left" valign="top">
-abs</td><td rowspan="3" align="left" valign="top">
-The absolute value of a number. abs(3) = abs(-3) = 3.
- abs() of a complex number is a complex number consisting of
- the absolute values of the real and imaginary parts, i.e.
- abs(a,b) = (abs(a),abs(b)).
-</td><td align="left" valign="top">
-Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td rowspan="3" align="left" valign="top">
-acos</td><td rowspan="3" align="left" valign="top">
-Inverse cosine function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-acosh</td><td rowspan="3" align="left" valign="top">
-Inverse hyperbolic cosine function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-alpha</td><td align="left" valign="top">
-The alpha component of a color. Can be assigned to.
-</td><td align="left" valign="top">
-Color
-</td><td align="left" valign="top">
-Float</td></tr><tr><td rowspan="3" align="left" valign="top">
-asin</td><td rowspan="3" align="left" valign="top">
-Inverse sine function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-asinh</td><td rowspan="3" align="left" valign="top">
-Inverse hyperbolic sine function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-atan</td><td rowspan="3" align="left" valign="top">
-Inverse tangent function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-atan2</td><td align="left" valign="top">
-The angle between this complex number and the real line,
- aka the complex argument.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td rowspan="3" align="left" valign="top">
-atanh</td><td rowspan="3" align="left" valign="top">
-Inverse hyperbolic tangent function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-blend</td><td align="left" valign="top">
-Blend two colors together in the ratio given by the 3rd parameter.
-</td><td align="left" valign="top">
-Color, Color, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td align="left" valign="top">
-blue</td><td align="left" valign="top">
-The blue component of a color. Can be assigned to.
-</td><td align="left" valign="top">
-Color
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-bool</td><td align="left" valign="top">
-Construct a boolean. It's not really required (bool x = bool(true) is just the same as bool x = true) but is included for consistency.
-</td><td align="left" valign="top">
-Bool
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-cabs</td><td align="left" valign="top">
-The complex modulus of a complex number z.
- cabs(a,b) is equivalent to sqrt(a*a+b*b).
- This is also the same as sqrt(|z|)
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td rowspan="2" align="left" valign="top">
-ceil</td><td rowspan="2" align="left" valign="top">
-Round up to the next highest number.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td rowspan="2" align="left" valign="top">
-cmag</td><td rowspan="2" align="left" valign="top">
-The squared modulus of a complex or hypercomplex number z.
- cmag(a,b) is equivalent to a*a+b*b. This is the same as |z|.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-color</td><td align="left" valign="top">
-Constructs a new color from floating point red, green, blue and alpha
- components. Equivalent to rgba.
-</td><td align="left" valign="top">
-Float, Float, Float, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td align="left" valign="top">
-complex</td><td align="left" valign="top">
-Construct a complex number from two real parts.
- complex(a,b) is equivalent to (a,b).
-</td><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-compose</td><td align="left" valign="top">
-Composite the second color on top of the first, with opacity given
-by the 3rd parameter.
-</td><td align="left" valign="top">
-Color, Color, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td rowspan="2" align="left" valign="top">
-conj</td><td rowspan="2" align="left" valign="top">
-The complex conjugate. conj(a,b) is equivalent to (a,-b).
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-cos</td><td rowspan="3" align="left" valign="top">
-trigonometric sine function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-cosh</td><td rowspan="3" align="left" valign="top">
-Hyperbolic cosine function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="2" align="left" valign="top">
-cosxx</td><td rowspan="2" align="left" valign="top">
-Incorrect version of cosine function. Provided for backwards
- compatibility with equivalent wrong function in Fractint.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-cotan</td><td rowspan="3" align="left" valign="top">
-Trigonometric cotangent function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-cotanh</td><td rowspan="3" align="left" valign="top">
-Hyperbolic cotangent function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-exp</td><td rowspan="3" align="left" valign="top">
-exp(x) is equivalent to e^x
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="2" align="left" valign="top">
-flip</td><td rowspan="2" align="left" valign="top">
-Swap the real and imaginary parts of a complex number.
- flip(a,b) = (b,a).
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-float</td><td align="left" valign="top">
-Construct a floating-point number.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td rowspan="2" align="left" valign="top">
-floor</td><td rowspan="2" align="left" valign="top">
-Round down to the next lowest number.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-fn1</td><td align="left" valign="top">
-Predefined function parameter used by Fractint formulas
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-fn2</td><td align="left" valign="top">
-Predefined function parameter used by Fractint formulas
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-fn3</td><td align="left" valign="top">
-Predefined function parameter used by Fractint formulas
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-fn4</td><td align="left" valign="top">
-Predefined function parameter used by Fractint formulas
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-gradient</td><td align="left" valign="top">
-Look up a color from the default gradient.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td align="left" valign="top">
-green</td><td align="left" valign="top">
-The green component of a color. Can be assigned to.
-</td><td align="left" valign="top">
-Color
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-hsl</td><td align="left" valign="top">
-Create a color from hue, saturation and lightness components. The alpha channel is set to to 1.0 (=100%).
-</td><td align="left" valign="top">
-Float, Float, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td align="left" valign="top">
-hsla</td><td align="left" valign="top">
-Create a color from hue, saturation and lightness components and an alpha channel.
-</td><td align="left" valign="top">
-Float, Float, Float, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td align="left" valign="top">
-hsv</td><td align="left" valign="top">
-Create a color from hue, saturation and value components. HSV is a similar color model to HSL but has a different valid range for brightness.
-</td><td align="left" valign="top">
-Float, Float, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td align="left" valign="top">
-hue</td><td align="left" valign="top">
-The hue of a color.
-</td><td align="left" valign="top">
-Color
-</td><td align="left" valign="top">
-Float</td></tr><tr><td rowspan="2" align="left" valign="top">
-hyper</td><td rowspan="2" align="left" valign="top">
-Construct a hypercomplex number with a real and 3 imaginary parts.
- Can be passed either 2 complex numbers or 4 floating-point numbers.
- hyper(a,b,c,d) is equivalent to the shorthand (a,b,c,d).
-</td><td align="left" valign="top">
-Float, Float, Float, Float
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-Complex, Complex
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-hyper_j</td><td align="left" valign="top">
-The 3rd component of a hypercomplex number. Can be assigned to.
- hyper_j(a,b,c,d) = c.
-</td><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-hyper_jk</td><td align="left" valign="top">
-The 3rd and 4th parts of a hypercomplex number.
- Can be assigned to. hyper_jk(a,b,c,d) = (c,d).
-</td><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-hyper_k</td><td align="left" valign="top">
-The 4th component of a hypercomplex number. Can be assigned to.
- hyper_k(a,b,c,d) = d.
-</td><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-hyper_ri</td><td align="left" valign="top">
-The real and imaginary parts of a hypercomplex number.
- Can be assigned to. hyper_ri(a,b,c,d) = (a,b).
-</td><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td rowspan="5" align="left" valign="top">
-ident</td><td rowspan="5" align="left" valign="top">
-Do nothing. ident(x) is equivalent to x.
- This function is useless in normal formulas but
- comes in useful as a value for a function parameter
- to a formula. For example, a general formula like z = @fn1(z*z)+c
- can be set back to a plain Mandelbrot by setting fn1 to ident.
- Note: ident() is compiled out so there's no speed penalty involved.
-</td><td align="left" valign="top">
-Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Bool
-</td><td align="left" valign="top">
-Bool</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="2" align="left" valign="top">
-imag</td><td rowspan="2" align="left" valign="top">
-Extract the imaginary part of a complex or hypercomplex number.
- imag(a,b) = b.
- imag() is unusual in that it can be assigned to: imag(z) = 7 changes
- the imag part of z.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-imag2</td><td align="left" valign="top">
-The square of the imaginary part of a complex number.
- real2(a,b) = b*b.
- While not a generally useful function, this is provided to ease porting
- of files from older Gnofract 4D versions.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-int</td><td align="left" valign="top">
-Construct an integer. To convert a float to an int, use floor, ceil, round or trunc instead.
-</td><td align="left" valign="top">
-Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td rowspan="3" align="left" valign="top">
-log</td><td rowspan="3" align="left" valign="top">
-The natural log.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-lum</td><td align="left" valign="top">
-The luminance (or brightness) of a color.
-</td><td align="left" valign="top">
-Color
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-manhattan</td><td align="left" valign="top">
-The Manhattan distance between the origin and complex number z.
- manhattan(a,b) is equivalent to abs(a) + abs(b).
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-manhattanish</td><td align="left" valign="top">
-A variant on Manhattan distance provided for backwards
- compatibility. manhattanish(a,b) is equivalent to a+b.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-manhattanish2</td><td align="left" valign="top">
-A variant on Manhattan distance provided for backwards
- compatibility. manhattanish2(a,b) is equivalent to (a*a + b*b)^2.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-max</td><td align="left" valign="top">
-Returns the larger of its two arguments.
-</td><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-max2</td><td align="left" valign="top">
-max2(a,b) returns the larger of a*a or b*b. Provided for
- backwards compatibility.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-mergemultiply</td><td align="left" valign="top">
-Multiplies colors together. Result is always darker than either input.
-</td><td align="left" valign="top">
-Color, Color
-</td><td align="left" valign="top">
-Color</td></tr><tr><td align="left" valign="top">
-mergenormal</td><td align="left" valign="top">
-Returns second color, ignoring first.
-</td><td align="left" valign="top">
-Color, Color
-</td><td align="left" valign="top">
-Color</td></tr><tr><td align="left" valign="top">
-min</td><td align="left" valign="top">
-Returns the smaller of its two arguments.
-</td><td align="left" valign="top">
-Float, Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-min2</td><td align="left" valign="top">
-min2(a,b) returns the smaller of a*a or b*b. Provided for
- backwards compatibility.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td rowspan="4" align="left" valign="top">
-neg</td><td rowspan="4" align="left" valign="top">
-No documentation yet.
-</td><td align="left" valign="top">
-Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-rand</td><td align="left" valign="top">
-Each time this is accessed, it returns a new pseudo-random complex number. This is primarily for backwards compatibility with Fractint formulas - use the random() function in new formulas.
-</td><td align="left" valign="top">
-
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td rowspan="2" align="left" valign="top">
-real</td><td rowspan="2" align="left" valign="top">
-Extract the real part of a complex or hypercomplex number.
- real(a,b) = a.
- real() is unusual in that it can be assigned to: real(z) = 7 changes
- the real part of z.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-real2</td><td align="left" valign="top">
-The square of the real part of a complex number.
- real2(a,b) = a*a.
- While not a generally useful function, this is provided to ease porting
- of files from older Gnofract 4D versions.
-</td><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Float</td></tr><tr><td rowspan="3" align="left" valign="top">
-recip</td><td rowspan="3" align="left" valign="top">
-The reciprocal of a number. recip(x) is equivalent to 1/x.
- Note that not all hypercomplex numbers have a proper reciprocal.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td align="left" valign="top">
-red</td><td align="left" valign="top">
-The red component of a color. Can be assigned to.
-</td><td align="left" valign="top">
-Color
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-rgb</td><td align="left" valign="top">
-Create a color from three color components. The alpha channel is set to to 1.0 (=100%).
-</td><td align="left" valign="top">
-Float, Float, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td align="left" valign="top">
-rgba</td><td align="left" valign="top">
-Create a color from three color components and an alpha channel.
-</td><td align="left" valign="top">
-Float, Float, Float, Float
-</td><td align="left" valign="top">
-Color</td></tr><tr><td rowspan="2" align="left" valign="top">
-round</td><td rowspan="2" align="left" valign="top">
-Round to the nearest number (0.5 rounds up).
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-sat</td><td align="left" valign="top">
-The saturation of a color.
-</td><td align="left" valign="top">
-Color
-</td><td align="left" valign="top">
-Float</td></tr><tr><td rowspan="3" align="left" valign="top">
-sin</td><td rowspan="3" align="left" valign="top">
-trigonometric sine function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-sinh</td><td rowspan="3" align="left" valign="top">
-Hyperbolic sine function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="4" align="left" valign="top">
-sqr</td><td rowspan="4" align="left" valign="top">
-Square the argument. sqr(x) is equivalent to x*x or x^2.
-</td><td align="left" valign="top">
-Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-sqrt</td><td rowspan="3" align="left" valign="top">
-The square root.
- The square root of a negative float number is NaN
- (ie it is NOT converted to complex). Thus sqrt((-3,0)) != sqrt(-3).
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-tan</td><td rowspan="3" align="left" valign="top">
-trigonometric sine function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="3" align="left" valign="top">
-tanh</td><td rowspan="3" align="left" valign="top">
-Hyperbolic tangent function.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td align="left" valign="top">
-Hyper
-</td><td align="left" valign="top">
-Hyper</td></tr><tr><td rowspan="2" align="left" valign="top">
-trunc</td><td rowspan="2" align="left" valign="top">
-Round towards zero.
-</td><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr><tr><td rowspan="3" align="left" valign="top">
-zero</td><td rowspan="3" align="left" valign="top">
-Returns zero.
-</td><td align="left" valign="top">
-Int
-</td><td align="left" valign="top">
-Int</td></tr><tr><td align="left" valign="top">
-Float
-</td><td align="left" valign="top">
-Float</td></tr><tr><td align="left" valign="top">
-Complex
-</td><td align="left" valign="top">
-Complex</td></tr></tbody></table></div></div><div class="sect2" title="Symbols"><div class="titlepage"><div><div><h3 class="title"><a id="Symbols"></a>Symbols</h3></div></div></div><div class="informaltable"><table border="1"><colgroup><col /><col /><col /><col /></colgroup><thead><tr><th>Name</th><th>Description</th><th>Argument Types</th><th>Return Type</th></tr></thead><tbody><tr><td align="left" valign="top">
-#center</td><td align="left" valign="top">
-Where the center of the image is located on the complex plane
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#color</td><td align="left" valign="top">
-Set this from a coloring function to directly set the color instead of using a gradient
-</td><td>Color</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#fate</td><td align="left" valign="top">
-The fate of a point can be used to distinguish between different basins of attraction or whatever you like. Set this to a number from 2 to 128 to indicate that a different 'fate' has befallen this point. 0 indicates the point has diverged, 1 that it has been trapped, &gt;1 whatever you like. Can only be usefully updated in the #final section.
-</td><td>Int</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#index</td><td align="left" valign="top">
-The point in the gradient to use for the color of this point.
-</td><td>Float</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#inside</td><td align="left" valign="top">
-Set this in the final section of a formula to override whether a point is colored with the inside or outside coloring algorithm. This is mainly useful in conjuction with #fate.
-</td><td>Bool</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#magn</td><td align="left" valign="top">
-The magnification factor of the image. This is the number of times the image size has doubled, or ln(4.0/size)
-</td><td>Float</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#maxit</td><td align="left" valign="top">
-No documentation yet.
-</td><td>Int</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#maxiter</td><td align="left" valign="top">
-No documentation yet.
-</td><td>Int</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#numiter</td><td align="left" valign="top">
-The number of iterations performed.
-</td><td>Int</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#pi</td><td align="left" valign="top">
-The constant pi, 3.14159...
-</td><td>Float</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#pixel</td><td align="left" valign="top">
-The (X,Y) coordinates of the current point. When viewing the Mandelbrot set, this has a different value for each pixel. When viewing the Julia set, it remains constant for each pixel.
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#solid</td><td align="left" valign="top">
-Set this to true in a coloring function to use the solid color rather than the color map.
-</td><td>Bool</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#tolerance</td><td align="left" valign="top">
-10% of the distance between adjacent pixels.
-</td><td>Float</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#xypixel</td><td align="left" valign="top">
-The (X,Y) coordinates of the current point. When viewing the Mandelbrot set, this has a different value for each pixel. When viewing the Julia set, it remains constant for each pixel.
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#z</td><td align="left" valign="top">
-No documentation yet.
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-#zwpixel</td><td align="left" valign="top">
-The (Z,W) coordinates of the current point. (See #pixel for the other two coordinates.) When viewing the Mandelbrot set, this remains constant for each pixel on the screen; when viewing the Julia set, it's different for each pixel. Initialize z to some function of this to take advantage of 4D drawing.
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-@p1</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-@p2</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-@p3</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-@p4</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-@p5</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-@p6</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-maxit</td><td align="left" valign="top">
-No documentation yet.
-</td><td>Int</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-maxiter</td><td align="left" valign="top">
-No documentation yet.
-</td><td>Int</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-p1</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-p2</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-p3</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-p4</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-p5</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-p6</td><td align="left" valign="top">
-Predefined parameter used by Fractint formulas
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-pi</td><td align="left" valign="top">
-The constant pi, 3.14159...
-</td><td>Float</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-pixel</td><td align="left" valign="top">
-The (X,Y) coordinates of the current point. When viewing the Mandelbrot set, this has a different value for each pixel. When viewing the Julia set, it remains constant for each pixel.
-</td><td>Complex</td><td class="auto-generated"> </td></tr><tr><td align="left" valign="top">
-z</td><td align="left" valign="top">
-No documentation yet.
-</td><td>Complex</td><td class="auto-generated"> </td></tr></tbody></table></div></div></div><div class="sect1" title="Gnofract 4D Internals"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="internals"></a><span class="application">Gnofract 4D</span> Internals</h2></div></div></div><p>
-
-This section explains how <span class="application">Gnofract 4D</span> is structured. You don't need to know
-any of this to use the program, but it may come in handy if you want
-to change it or contribute to its development (which you're heartily
-encouraged to do).
-</p><p>
-
-<span class="application">Gnofract 4D</span> is implemented primarily in Python, with some C++
-extensions. Extensive use
-is made of Python unittest framework to keep everything working - each
-Python file <code class="filename">foo.py</code> is accompanied by
-<code class="filename">test_foo.py</code>, which contains unit tests for that
-file's features. 'test.py' for each folder runs all of the tests.
-</p><div class="sect2" title="Source Code Layout"><div class="titlepage"><div><div><h3 class="title"><a id="layout"></a>Source Code Layout</h3></div></div></div><p>
-The important directories in the source are:
-
-</p><div class="informaltable"><table border="1"><colgroup><col /><col /></colgroup><thead><tr><th>Directory</th><th>Contents</th></tr></thead><tbody><tr><td><p><code class="filename">fract4d</code></p></td><td> <p>This contains all the non-GUI-related, relatively
-platform-independent parts of the code. This is in case it ever needs
-to be ported to another environment (eg run on a server without a GUI
-as part of a cluster). Most of the files here are parts of the
-compiler (see below). The main class which represents a fractal is in
-<code class="filename">fractal.py</code>. This holds references to the compiled
-code, the formula and colorfunc definitions, the parameters and the
-colormap. It also handles loading and saving information from a
-<code class="filename">.fct</code> file, and provides
-wrappers for some of the gnarlier C++ extension functions. </p>
-</td></tr><tr><td><p><code class="filename">fract4d/c</code></p></td><td> <p>This contains the C++ extension code which is compiled
-to produce <code class="filename">fract4dc.so</code>. This is divided into a
-set of classes which communicate primaily via interfaces. The main
-responsibility of this code is to call the 'pointFunc' (the function
-which calculates a single pixel) once for each point on the
-image. This code also does the bulk of the '4D' manipulation -
-<code class="filename">vectors.h</code> contains code for 4-vectors and 4x4
-matrix math. This library also handles multi-threaded calculations,
-parcelling out the work to multiple MTFractWorkers via the queue in
-<code class="filename">threadpool.h</code></p> </td></tr><tr><td><p><code class="filename">fract4dgui</code></p></td><td> <p>This contains the python code which implements the
-GUI. It uses PyGTK as the GUI toolkit. The earliest PyGTK we support
-is 1.99, which has some annoying incompatibilities with newer PyGTK's
-like 2.4. I need to work out whether to ditch the older library
-altogether or try to come up with some wrappers to hide the
-differences. Basically there's one class per dialog or custom control,
-and a few other for utility purposes. The central class is
-<code class="classname">gtkfractal</code>, which wraps a
-<code class="classname">fractal</code> and displays the results of the
-calculation in a window. </p> </td></tr><tr><td><p><code class="filename">fract4dgui/c</code></p></td><td> <p>This contains the C code which implements the
-fract4dguic.so extension. This only has one minimal function, to
-obtain gconf settings. </p> </td></tr></tbody></table></div><p>
-
-</p></div><div class="sect2" title="Compiler"><div class="titlepage"><div><div><h3 class="title"><a id="compiler_internals"></a>Compiler</h3></div></div></div><p>The most complicated part of <span class="application">Gnofract 4D</span> is the compiler. This takes
-as input an UltraFractal or Fractint formula file, and produces C
-code. We then invoke a C compiler (eg gcc) to produce a shared library
-containing code to generate the fractal which we dynamically load.
-</p><p>
-The UltraFractal manual is the best current description of the formula
-file format, though there are some UltraFractal features which are not
-yet supported. You can download it from <a class="ulink" href="http://www.ultrafractal.com/uf3-manual.zip" target="_top">here</a>.
-</p><p>
-The implementation is based on the outline in <em class="citetitle">Modern Compiler Implementation in ML: basic
-techniques</em> (Appel 1997, Cambridge). It doesn't do any
-optimization at this point, leaving that to the C compiler used as a
-back-end. It would be worthwhile to do some simple optimization (eg
-constant-folding, removing multiplication by 1.0) because the C
-compiler refuses to do this to floating point numbers.</p><p>
-Overall structure: The <a class="ulink" href="http://www.dabeaz.com/ply/ply.html" target="_top">PLY</a> package
-is used to do lexing and SLR parsing - it's in
-<code class="filename">lex.py</code> and
-<code class="filename">yacc.py</code>. <code class="filename">fractlexer.py</code> and
-<code class="filename">fractparser.py</code> are the lexer and parser
-definitions, respectively. They produce as output an abstract syntax
-tree (defined in the <code class="classname">Absyn</code> module). The
-<code class="classname">Translate</code> module type-checks the code,
-maintains the symbol table (<code class="filename">symbol.py</code>) and
-converts it into an intermediate form (<code class="filename">ir.py</code>).
-<code class="classname">Canon</code> performs several simplifying passes on
-the IR to make it easier to deal with, then
-<code class="classname">codegen</code> converts it into a linear sequence of
-simple C instructions. <code class="filename">stdlib.py</code> contains the
-'standard library' of mathematical functions, like cosh(z). It's at
-this point that complex and hypercomplex variables are expanded out
-into pairs of floating point numbers - the C code is oblivious to the
-complex numbers. Finally we invoke the C compiler to convert to a
-native code shared library.</p><p>
-At runtime the different phases happen at different times. First, the
-entire .frm file is lexed and parsed. Then when a particular formula
-is selected, it's translated and syntax-checked. The actual code is
-only generated just before the fractal is drawn. This phase is
-repeated whenever the function parameters are changed (eg @fn1 is set
-to 'cosh').
-</p><p>
-Probably the ugliest part of the code is the handling of
-parameters. Numeric parameters like floats are passed in as an array,
-and the C++ code and Python code need to collaborate to work out which
-indices into this array correspond to which params- this is done by
-sorting them into alphabetic order. In general this area is a bit of a
-mess.</p></div><div class="sect2" title="Threading"><div class="titlepage"><div><div><h3 class="title"><a id="threading"></a>Threading</h3></div></div></div><p>
-One of the weirder parts of the code is how we deal with
-threading. Basically we want the calculation of the fractal to happen
-on a different thread (or multiple threads for SMP) from the main UI,
-so you can interrupt at any point. This is complicated by the fact
-that Python only allows a single thread in the Global Interpreter
-Lock, and that PyGTK is often compiled by Linux distribution vendors
-without thread support, meaning this lock is not released when running
-the GTK main loop.
-</p><p>
-The way out of this is that the additional threads live only in the
-C++ code, where they are invisible to the Python code and GTK. When
-<code class="function">pycalc</code> is called with async=True, it spawns a
-thread to do the calculation, which may in turn spawn more workers if
-we want multiple threads. These all write to the image buffer and
-report back what they're doing by writing messages into a pipe. This
-pipe is added to the list of things the GTK main loop monitors, so
-whenever a new message appears we get a callback into the gtkfractal
-code, interleaved with the normal GTK events. We can interrupt a
-calculation in progress by setting a var which the calculation threads
-check frequently - they then abandon their work and quit. </p><div class="warning" title="Warning" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Warning</h3><p> Multiple threads and C++ exceptions do not coexist
-well, at least on some of the libstdc++'s that <span class="application">Gnofract 4D</span> runs with. So the
-C++ code can't throw exceptions or very odd things including crashes
-will happen. </p></div></div></div><div class="sect1" title="Bugs and Known Issues"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="bugs"></a>Bugs and Known Issues</h2></div></div></div><div class="sect2" title="Reporting Bugs"><div class="titlepage"><div><div><h3 class="title"><a id="reporting"></a>Reporting Bugs</h3></div></div></div><p>
-<span class="emphasis"><em>Please</em></span> report any bugs you encounter, either by
-mailing <a class="ulink" href="mailto:catenary@users.sourceforge.net" target="_top">
-catenary@users.sourceforge.net</a> or by
-using the <a class="ulink" href="http://sourceforge.net/tracker/?func=add&amp;group_id=785&amp;atid=100785" target="_top">
-bug form</a> at SourceForge. I'll do my best to fix them. </p></div><div class="sect2" title="Backwards Compatibility"><div class="titlepage"><div><div><h3 class="title"><a id="compat"></a>Backwards Compatibility</h3></div></div></div><p>
-Version 2.x contains major architectural changes from version 1.x, so
-unfortunately not all images generated by earlier versions will look
-exactly the same or even load correctly. If you have a favorite image
-which doesn't work any more, mail me the .fct file and I'll try and
-convert it. I hope to fix most of these issues in future versions.
-</p><p>
-Specific known issues:
-</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"><p> Files generated by <span class="application">Gnofract 4D</span> versions older than
-1.4 can't be loaded. </p></li><li class="listitem"><p> Only one colormap per file is supported (the outer
-one). Inner colormaps are ignored. </p></li></ul></div><p>
-
-</p></div></div><div class="sect1" title="About Gnofract 4D"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="about"></a>About <span class="application">Gnofract 4D</span></h2></div></div></div><p>
-
-This is <span class="application">Gnofract 4D</span> version 3.14.1. You can find the most recent version of
-<span class="application">Gnofract 4D</span> from <a class="ulink" href="http://gnofract4d.sourceforge.net" target="_top">
-http://gnofract4d.sourceforge.net/</a>.
-</p><div class="sect2" title="Credits and copyright"><div class="titlepage"><div><div><h3 class="title"><a id="credits"></a>Credits and copyright</h3></div></div></div><p>
-<span class="application">Gnofract 4D</span> is Copyright 1999-2009 Tim Whidbey <a class="ulink" href="mailto:catenary@users.sourceforge.net" target="_top">(catenary@users.sourceforge.net)
-</a>, and is distributed under the <span class="emphasis"><em>BSD
-license</em></span>. See the file "COPYING" for details.
-</p><p>
-<span class="application">Gnofract 4D</span> was originally based on Gnofract, written by Aurelien Alleaume
-<a class="ulink" href="mailto:manchot@club-internet.fr" target="_top">(manchot@club-internet.fr)
-</a>,
-though none of the original code remains in the current version.
-Gnofract could once be obtained from
-<a class="ulink" href="http://www.multimania.com/mason/" target="_top">
-http://www.multimania.com/mason/</a> but this no longer appears to
-work.
-</p><p>
-Branko Kokanovic developed and contributed the animation
-feature. Chris Le Sueur provided parts of the gradient editing
-feature. Henryk Trappmann provided HSV gradient support.
-The man page was contributed by Aleksander Adamowski.</p><p>
-The formula language which <span class="application">Gnofract 4D</span> uses originated in <span class="application">Fractint</span> and
-was substantially enhanced in <span class="application">UltraFractal</span>. However the compiler
-implementation does not share any code with those programs.
-</p><p>
-The <span class="application">Gnofract 4D</span> distribution contains palette (.map) files by a number of
-authors which were originally distributed with <a class="ulink" href="http://spanky.triumf.ca/" target="_top"><span class="application">Fractint</span></a> under somewhat murky
-licensing conditions. It also contains a copy of "standard.ucl",
-originally distributed with <a class="ulink" href="http://www.ultrafractal.com/" target="_top"><span class="application">UltraFractal</span></a>, by kind
-permission of Frederik Slijkerman, Damien Jones, and Kerry Mitchell.
-"blatte1.ugr" and "blatte2.ugr" are included by kind permission of
-<a class="ulink" href="http://exoteric.roach.org/" target="_top">'Blatte'</a>. The formulas
-in Sterling2.frm are translations of formulas originally created by
-Tad Boniecki for use with the SterlingWare 2 fractal program.
-</p><p>
-<code class="filename">gmpy.c</code> and <code class="filename">gmpy.h</code> are from
-the GMPY package (http://gmpy.sf.net), and are distributed under the
-LGPL license. </p><p>
-<code class="filename">lex.py</code> and <code class="filename">yacc.py</code> come from
-the PLY package, and are distributed under the LGPL license. </p><p>
-Some of the menu icons are taken or adapted from
-the <a class="ulink" href="http://tango.freedesktop.org" target="_top">Tango icon set</a>.
-</p></div></div></div></body></html>
diff --git a/gnofract4d.install b/gnofract4d.install
deleted file mode 100644
index f7e1473bf9e..00000000000
--- a/gnofract4d.install
+++ /dev/null
@@ -1,12 +0,0 @@
-post_install() {
- update-desktop-database -q
- update-mime-database usr/share/mime &>/dev/null
-}
-
-post_upgrade() {
- post_install $1
-}
-
-post_remove() {
- post_install $1
-}