Welcome to my page dedicated to fractals! Here (when I get around to adding things) you will find information about fractals and links to resources, blog posts, and anything else I stumbled across on the internet related to fractals.

- What Are Fractals?
- General Information
- Research and Papers
- Software
- Resources
- Communication Hubs
- Personal Sites

This could be a doctoral thesis. The definition has sort of evolved but all of these things are essentially related by a simple principle from which they all sprung. Ready for this?

"Fractal" is an abbreviation for "fractional dimension" and is a term coined by Benoit Mandelbrot. A fractal structure in classic geometry is one that, while clearly possessing an edge, has an edge that is so rough it appears to partially occupy another dimension. It is mathematically continuous but not differentiable. The characteristic visual feature of a fractal is that, no matter how close you look at its surface, you can never really find its edge, even though there is clearly a distinct area on one side of the surface and a distinct area on the other side.

The easiest way to create a fractal is by creating ever smaller iterations of a shape all attached to the surface of their larger originals and repeating this process ad infinitum. This results in the self-similarity characteristic of many fractals you may see.

In artwork, we attempt to perform this self-similarity algorithm as far as we are visually capable. Since humans have trouble doing this by-hand, we often use computers and iterate structures until the graininess of the fractal's edge is as small as we can render.

Physical reality contains a number of pseudo-fractals - things that, for the most part, fulfill the definition as far as human observation can tell while not technically being infinite in graininess. Some examples include clouds, trees, grass lawns, rock formations, paths of streams flowing into rivers. There may be a half-dozen recognizable pseudo-fractals beside you right now!

Human life has dozens of fractals, the most recognizable being things like morality and ethics, brain states, politics, economics, and even your daily routine. Some you probably think less of include the number of possible ways to peel a potato, organize your memoirs, and greet a Martian. (The fractional dimension is in the subtle ways you can change doing each of these activities while still technically performing the same event.)

There are also philosophical conjectures that resemble fractals. Zeno's Paradox is one.

- Flam3 - the site of Scott Draves, creator of the Flam3 algorithm.

I've collected some old links from the Aposhack and saved them here, primarily for historic reference.

*What Are Fractals | Explain Like I'm Five*- Reddit discussion.- Basics of using Apophysis
*What is a fractal*- Gif file demonstration of a fractal tree's self-replication feature.

- Flam3 description - paper by Scott Draves. It is the origin of the fractal flame software algorithm that most fractal flame programs still use.
*Fractal Dimension and Exponential Folding of Chaotic Manifold*by H. Rafat and F. Salama of Tanta Univ. in Egypt. Their explanation of a "fractal" is excellent.

These days, fractal software has resulted in a public understanding of fractals that has deviated from the original definition. People think that if it's made with a software program capable of making fractals then it must be a fractal. That's wrong, but no doubt, there are some very odd looking structures that do (bizarrely enough) fulfill the definition (at least as a pseudo-fractal, since that's all we can do on the computer).

That said, there are a number of programs you can use to create fractals. As there are always more being created, I can't keep track of them all. Those that don't appear to be supported or don't have much functionality may not be included on this list.

- JWildfire - (Source code) A feature rich fractal creation suite written in Java.
- Electric Sheep - Mutating fractals screensaver that communicates with other computers and enables user voting to create beautiful fractals.
- Apo 7X - Fractal flame creation software.
- Fractor3 (source code) - Escape-time fractal creator written in Java.
- software by Element90 - Escape-time fractal exploration and rendering programs, such as Saturn and Titan. Saturn and Titan articles. If you look around, there is some explanation for the madness in the names for the transforms.
- FractalNow - A multi-threaded fractal explorer.
- Apophysis - The original Apophysis (delphi application) for creating fractals. Home page.
- Mandelbulb3D
- Mandelbulber
- Flam4 - a GPU flame fractal renderer

- Chaotica - Fractal flame creation with emphasis on 2D-fractal rendering quality.
- Ultra Fractal - Fancy decoration of escape-time fractals.
- Frax - Fractal creation App for Apple devices.
- Fractal Architect - Fractal creation software for Mac.
- Jux - Julia and Mandelbrot exploror for Windows with colorful effects. No scripting.
- fractal tree creator - small donationware application for Windows

- Xenodream - for creating iterative meshes and fractals

*Rosetta Code*: Fractal Tree - How to create a fractal tree in every programming language.- Mandelbrot in the programming language of Charly

Mandelbrot in the programming language of Charly, by Leonard Schütz:

```
60.times(func(a) {
180.times(func(b) {
let x = 0
let y = 0
let i = 0
while !(x ** 2 + y ** 2 > 4 || i == 99) {
x = x ** 2 - y ** 2 + b / 60 - 1.5
y = 2 * x * y + a / 30 - 1
i += 1
}
if i == 99 {
write("#")
} else if i <= 10 {
write(" ")
} else {
write(".")
}
})
write("\n")
})
```

I'll update this eventually.

There are a number of videos on youtube, including some that I've posted, but I plan on selecting a few that I think are the most helpful. And hey, I could be biased... XD This list will be updated slowly.

- The Aposhack Plugins Pack - A collection of plugins compatible with Apophysis 7x. Direct links are below. (Note: All these links may become outdated in the near future.)
- Apo Plugins Starter Pack - A smaller version of the Aposhack Plugins Pack. This one contains most of the useful plugins you will need if they are not already included with your software.

There were a number of groups on DeviantArt for sharing resources. I don't have an exhaustive list. Some groups have gone defunct.

*Fractal Forums*- The internet hub of fractal discussion.*JWildfire Forum*- Official forum for the software.*/r/Fractals*- Semi-active reddit channel.

A great deal of discussion about fractal flames used to occur on DeviantArt, especially at Aposhack. As DeviantArt has started to wain, activity has sinced diminished. More recently, someone started a Slack channel for discussion.

- Sign up form for the new Slack channel. Posted fall 2016.

Active groups on DeviantArt:

*XtremeFractals2*(The original has been closed and saved as an archive.)*FractalDreams**AllThingsFractal**FractalMuseum*

- personal site of Inigo Quilez - Contains articles on 3D graphics, including articles about rendering both 2D and 3D fractals.