You will probably be familiar with some of the most famous fractals, such as the Mandelbrot set, Sierpinski triangle, or Lorenz Attractor.
Types of fractal
There are a number of different types of fractals, but they all tend to have certain things in common:
- Fractals tend to have complex shapes.
- The shapes often possess infinite amounts of detail, which means that you can zoom in on the shape forever and there will always be more detail.
- They are often self-similar at different scales, that is as you zoom in the image will have similar features to the original image.
- They are often created by very simple formulas.
There are several different ways to create fractals:
- Strange attractors, such as the Tinkerbell fractal covered below.
- Escape time fractals, such as the Mandelbrot fractal also covered below.
- Iterated function systems
- Grammar based systems, such as L-systems and finite subdivision rules.
- Random fractals, such as fractal landscapes and diffusion limited aggregation.
We will cover strange attractors and escape time fractals in this section, because they have similar implementations.
Here are some strange attractors and escape time fractals that can be created with generativepy: