Michele Mantovan

Generative Art #2 – Fractals

In this Generative Art post I’d like to talk a little about fractals. But first a little disclaimer: this post is not intended to be exhaustive on the matter, this argument would need more readings and researches after reading this post, which is intended to be only an introduction on the matter. Ok, now let’s dive in.

What is a fractal?

There are different ways you can frame fractals to understand what they are but here, I will frame them mainly mathematically and graphically. As a general definition, a fractal is “an abstract object used to describe naturally occurring objects” (Wikipedia). They have a lot of applications, from technology to medicine and even archeology.
Since fractals can be found in nature, over the years a lot of mathematicians tried (with different degrees of success) to give fractals a formal definition, and they articulated all the work in mathematical formulas and equations to describe different types of fractals.
Most of these formulas involves complex numbers, exponentials and they could be very hard to understand. This image right here is an example of fractals in nature, broccoli.

Types of fractals

There are a lot of different types of fractals (HERE) out there, but only some of them are also visually interesting. Some of the most famous fractals typology used for graphical matters are the Mandelbrot set, the Apollonian gasket, the Julia set, and the dragon curve. Here are a couple of examples:

The flame algorithm

One of the most popular fractal generated with computers that can be visually interesting are the so called “flames”. This name comes from the open-source algorithm that was invented by Scott Draves and Erik Reckase (HERE). Since the algorithm became open-source, over the years a big community around this has started to grow and a lot of applications to create visual fractals has the flame algorithm in it. Here some examples of what flames can look like.

Program to use

There are a lot options on what you can use to create fractals. Some programs are outdated but still functioning and some others are more recent, some of them uses CPU and some others use GPU, some of them are specialised on certain types of fractals and others are more generic. Here you can find some popular options:

  • Apophysis: free tool to create fractals illustrations (mostly flames). Open-source and only for Windows (try the 3D version to create 3D fractals).
  • Chaotica: commercial and multi-platform software to create different types of fractal illustrations.
  • Electric ship: to create fractal-animation videos like the following example.

Fractals aren’t easy to understand and I know that after reading this post probably you are more confused than before, but the more you use the softwares and the more you dive deep into the matter, the more you can understand it. There is also a great community that you can interact with. I found them on DeviantArt and they invited me in they fractal Discord channel they have, which is great for asking questions and gathering a lot of information.