In this definition you can model a fractal based on a square which builds two smaller squares on one of its edges.
In this definition you can make a fractal rotating polygon by using the Anemone plugin. First we are going to explode the curve to its segments and then evaluate a point on the edges. This recursive algorithm will produce the final rotating polygons.
Civilization has struggled to understand this perfect geometry for thousands of years. In the 4th century, Plato believed that symmetry in nature was proof of universal forms; in 1952, the famous code-breaker Alan Turing wrote a book trying to explain how such patterns in nature could be formed.
Mandelbrot set, a famous fractal that is a badge of honor for mathematicians. One way of defining the Mandelbrot set is by looking at how complex functions behave under repeated iteration.
This video by Softology is about 3d cellular automata. 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 fractal enthusiasts to tweak and customise to their needs.