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| -rw-r--r-- | .SRCINFO | 24 | ||||
| -rw-r--r-- | PKGBUILD | 54 | ||||
| -rw-r--r-- | gnofract4d-manual.html | 1825 | ||||
| -rw-r--r-- | gnofract4d.install | 12 |
4 files changed, 29 insertions, 1886 deletions
@@ -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 @@ -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 07706d7e5d63..000000000000 --- 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><cursor></strong></span> to move more -quickly. Hold down <span class="keycap"><strong>Shift</strong></span> + -<span class="keycap"><strong><cursor></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> > <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> -> <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| < 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| < 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><</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><</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><</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"> -&&</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"> -<</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"> -<=</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"> -></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"> ->=</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, >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&group_id=785&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 f7e1473bf9e0..000000000000 --- 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 -} |