Apophysis is an open source fractal flame editor and renderer writen in delphi around 2004. It has become very popular and there are several versions adding new features like 3D and 64 bit support.
Apophysis 7X “A version of the fractal flame editor Apophysis which is ready to take advantage of modern versions of Microsoft Windows, provides a big set of new features and has a polished user interface.” Modern Windows here refers to Windows 7.
Apophysis AV “Apophysis AV is an improved and modern version of the famous fractal flame editor Apophysis. This application combines the best options of previous branches (e.g. 3D- or 64-bit support and favourite variations), some of which were lost in the development process, and has multiple bugfixes. Besides, Apophysis AV has a lot of new features.” (2021)
New variation may be added in form of plugins (deviantArt group for plgins).
“Fractorium is a free editor and renderer for creating images and animations using the fractal flames algorithm. In addition to the standard rendering method on the CPU, it allows for using the GPU if supported hardware is present.”
“Chaotica is a next-generation fractal art application, designed for both novices and professional artists. Novice users can enjoy editing randomised fractals to produce stunning HD wallpapers and animations. Professional users will particularly value the fast, modern rendering engine. High quality animations and huge images for print are easily produced, with real-time imaging controls that will dramatically accelerate your workflow.”
Chaos helper applies gradients to chaotica files.
IFSRenderer is a 3D IFS fractal GPU-powered renderer with node-based editor which provides visual representation of the fractal structure.
JWildfire “is the spiritual successor of the award winning image-processing software Wildfire\7PPC for the Amiga. But, this time implemented using a high-level language (Java), with a more sophisticated user interface, and much more cool effects, and flame fractals.”
Flam3 (github) Open source fractal flame renderer written in C in the 90s. Used by electric sheep, qosmic and fr0st.
PDF descriing the fractal flame algirithm
Mandelbulber and Mandelbulb3D
Two simillar programs for creating and exploring 3D fractal scenes using differents formulas, materials and lighting.
deviantArt groups: mandelbulbfractals, mandelbulbers, mandelbulbs, m3d-parameters, mandelbulb3D
“Incendia is a 3D fractal program that uses Iterated Function Systems (IFS) for 3D fractal generation. It also uses several parametric surfaces in order to build complex fractal structures.”
“With Ultra Fractal, you can choose from thousands of fractal types and coloring algorithms, zoom in as far as you want, use gradients to add color, and apply multiple layers to combine different fractals in one image.”
DeviantArt groups: ultra-fractal-redux, uf-artists
“XaoS lets you dive into fractals in one fluid, continuous motion. It has many other features like a wide array of different fractal types and coloring modes, autopilot, random palette generation, color cycling, and animated tutorials.”
“Want to create DEEP Mandelbrot fractals 100 times faster than the commercial programs, for FREE? One hour or one minute? Three months or one day? Try Kalles Fraktaler!”
Kalles Fraktaler 2
Kalles Fraktaler 2 +
And many others:
“Gnofract 4D is a free, open source program which allows anyone to create beautiful fractal images. These include the famous Mandelbrot and Julia sets and many more. You can explore a universe of images just using a mouse.”
“Jux is a fractal explorer for 2D Julia and Mandelbrot sets. It includes a variety of formulas. It has beautiful coloring and lighting effects. It is easy to use. There is no formula editor or scripting.”
“Mandelbrot Explorer is free software, allowing the exploration of the Mandelbrot Set and the Julia Sets.”
FragM is a maintained fork of Fragmentarium, “open source, cross-platform IDE for exploring pixel based graphics on the GPU”.
Visions of Chaos
“Visions of Chaos is a professional high end software application for Windows. It is simple enough for people who do not understand the mathematics behind it, but advanced enough for enthusiasts to tweak and customise to their needs. It is the most complete all in one application dealing with Chaos Theory and Machine Learning available.”
IFStile you can explore tiles and export them in .flame format. There is also online version.
Structure Synth is a cross-platform application for generating 3D structures by specifying a design grammar.
Chaoscope is a 3D strange attractors rendering software.
“Terragen™ is a powerful solution for building, rendering, and animating realistic natural environments.”
G’MIC is an open-source framework for digital image processing. It can be also used to generate fractals.
FractalLab - interactive WebGL fractal explorer