diff options
| author | willemw12 | 2015-06-09 13:34:09 +0200 |
|---|---|---|
| committer | willemw12 | 2015-06-09 13:34:09 +0200 |
| commit | 5e48a70fcf5298657f629d06cadbb51abdbb0754 (patch) | |
| tree | 4c127704c401fbc27906a52978d444a778633484 | |
| download | aur-5e48a70fcf5298657f629d06cadbb51abdbb0754.tar.gz | |
Initial commit
| -rw-r--r-- | .SRCINFO | 20 | ||||
| -rw-r--r-- | PKGBUILD | 60 | ||||
| -rw-r--r-- | gnofract4d-manual.html | 1825 | ||||
| -rw-r--r-- | gnofract4d.install | 12 |
4 files changed, 1917 insertions, 0 deletions
diff --git a/.SRCINFO b/.SRCINFO new file mode 100644 index 000000000000..d09ca06bbbfd --- /dev/null +++ b/.SRCINFO @@ -0,0 +1,20 @@ +pkgbase = gnofract4d + pkgdesc = Create beautiful fractal images in PyGTK + pkgver = 3.14.1 + pkgrel = 3 + url = http://gnofract4d.sourceforge.net + install = gnofract4d.install + arch = any + license = BSD + makedepends = docbook-xsl + depends = desktop-file-utils + 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 + +pkgname = gnofract4d + diff --git a/PKGBUILD b/PKGBUILD new file mode 100644 index 000000000000..87753e2b3a44 --- /dev/null +++ b/PKGBUILD @@ -0,0 +1,60 @@ +# Maintainer: willemw <willemw12@gmail.com> +# Contributor: Limao Luo <luolimao+AUR@gmail.com> +# Contributor: sausageandeggs <sausageandeggs@archlinux.us> +# 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_${pkgver//./_}" +pkgrel=3 +pkgdesc="Create beautiful fractal images in PyGTK" +arch=('any') +url="http://gnofract4d.sourceforge.net" +license=('BSD') +makedepends=('docbook-xsl') +depends=('desktop-file-utils' 'libjpeg' 'libpng' 'pygtk') +install=$pkgname.install +source=(https://github.com/edyoung/gnofract4d/archive/$_pkgver.tar.gz + gnofract4d-manual.html) +md5sums=('0872b6acefa9123205e099c9e174a791' + '784e9aeb0abcf473d338481f37503ab0') + +prepare() { + cd $pkgname-$_pkgver + + 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|" \ + 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 +} + +#check() { +# cd $pkgname-$_pkgver +# python2 test.py +#} + +package() { + cd $pkgname-$_pkgver + python2 setup.py install --root="$pkgdir" --optimize=1 + install -Dm644 COPYING "$pkgdir/usr/share/licenses/$pkgname/COPYING" + install -Dm644 doc/gnofract4d.1 "$pkgdir/usr/share/man/man1/$pkgname.1" + + # Patch for createdocs.py. Generating "Formula Reference Reference" entries fails: + # Erro: no refentry: No refentry elements found in "Gnofract 4D". Gnofract 4D + install -m644 "$srcdir/gnofract4d-manual.html" "$pkgdir/usr/share/gnome/help/gnofract4d/C/gnofract4d-manual.html" +} + diff --git a/gnofract4d-manual.html b/gnofract4d-manual.html new file mode 100644 index 000000000000..07706d7e5d63 --- /dev/null +++ b/gnofract4d-manual.html @@ -0,0 +1,1825 @@ +<?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 new file mode 100644 index 000000000000..f7e1473bf9e0 --- /dev/null +++ b/gnofract4d.install @@ -0,0 +1,12 @@ +post_install() { + update-desktop-database -q + update-mime-database usr/share/mime &>/dev/null +} + +post_upgrade() { + post_install $1 +} + +post_remove() { + post_install $1 +} |