The Fractal Page

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.

  1. What Are Fractals?
  2. General Information
  3. Research and Papers
  4. Software
  5. Resources
  6. Communication Hubs
  7. Personal Sites

What Are Fractals?

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.

General Information

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

Research and Papers


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.





Mandelbrot in the programming language of Charly, by Leonard Sch├╝tz:

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 {
    } else if i <= 10 {
      write(" ")
    } else {




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.

Parameters, Gradients, Shared Files

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

Communication Hubs

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.

Active groups on DeviantArt:

Personal Sites