The focus of this category is on software designed to generate images of fractals, both free and commercial.
A fractal is a geometric shape that forms a never-ending pattern, infinitely complex patterns that repeat a simple process over and over in an ongoing feedback loop. A small extract of the fractal shape will look the same as the entire shape, a property known as self-similarity.
To create a fractal, you begin with a simple pattern and repeat it at small scales, again and again, forever. Of course, in real life it's impossible to draw fractals with infinitely small patterns, but we can draw shapes that look like fractals.
In nature, fractals are found in trees, waterways, coastlines, mountains, clouds, seashells, lightning, and hurricanes.
While fractals can be modeled, the range of scales possible is considerably less than infinite, given the practical limits of time and space. However, models can simulate theoretical fractals or natural phenomena with fractal features. Images and other outputs of modeling are frequently referred to as being fractals although they lack strictly fractal characteristics and depth.
Computer programmers have used various mathematical programming languages to create fractals. However, there are several fractal-generating software applications available, open-source and proprietary. Using software, users can create mathematical beauty through visualization, which describes the aesthetics derived from the abstractness, purity, simplicity, depth, and orderliness of mathematics.
Fractal-generating software packages use a variety of methods for creating fractals. Most of them include an algorithm selection, zoom options, and the ability to save in a variety of formats, such as JPG, TIFF, or PNG, as well as parameter files, so that the user can easily return to previously created fractals for later modification.
Most packages allow the user to choose a maximum iteration so that the iteration can be increased when the image is magnified, so as not to lose any fine detail. Limiting the maximum iterations may be necessary when the computer's processing power is low.
There may also be coloring options, such as color randomization and color density, as well as post-processing layering. Both 2D and 3D rendering effects may also be included.
Fractal-generating features are available in some standard graphics packages, such as GIMP and Blender, while some standalone fractal-generating programs can be integrated with Photoshop to allow for the creation of more complex images.
Even with the software, generating fractals can be difficult to master. Due to the butterfly effect, a small change in one variable can have an unpredictable effect. Many of the software-generating packages have a steep learning curve. Most of the programs generate 2D fractal, while some can be used to create 3D fractal objects.
Any software application or package designed to generate fractals is appropriate for this category.
Recommended Resources
The free and open-source Windows application is available through the terms of the GNU General Public License, including its source code. It is a fractal flame editor and renderer that includes several features for creating and editing fractal flames, as well as a scripting language with direct access to most of the components of the fractal. Development notes and project samples are presented, along with reviews, user ratings, and a support forum area.
https://sourceforge.net/projects/apophysis/
Developed by Glare Technologies, Chaotica is a commercially available fractal art editor and renderer, designed for novices as well as professional artists, that can be used to extend the functionality of Apophysis. A free version is also available, although it offers limited render resolution and animation length. A gallery of arts shows the capabilities of the software, and a user’s manual is available, along with an informational blog, and community support forum.
https://www.chaoticafractals.com/
Originally released in 1999, and available for Linux, Mac, and Windows, Electric Sheep is a distributed computing project by Scott Draves, intended for animating and evolving fractal flames, which are then distributed to networked computers which display they as a screensaver. The process is transparent to the casual user, who can simply install the software as a screensaver. However, the user may opt to get involved with the project, creating a fractal flame file for upload.
https://electricsheep.org/
Hosted on GitHub, Gnofact 4D is a free and open-source software program used to create images called fractals, which are automatically generated by the computer, based on mathematical principles, which include the Mandelbrot and Julia sets, as well as others. Designed to be easy to use, fast, and flexible, the program is compatible with Unix-based systems like Linux and FreeBSD, as well as macOS. It is available through the BSD license.
http://edyoung.github.io/gnofract4d/
Available as a free trial version for thirty days, Ultra Fractal is designed to operate on the macOS platform. The downloaded evaluation version is fully functional, except that exported and rendered images are marked as an evaluation copy. The purchase of a license turns the trial version into a full version. Its features are listed, along with screenshots, a PDF manual is available, along with its system requirements, development notes, and support data. A support forum is included.
https://www.ultrafractal.com/
