Fractals

Martin McBride
2021-12-14

These articles demonstrate various fractals, created using generativepy.

There are several common methods of creating fractals:

  • Iterated function systems (IFS) - these use geometric replacement rules, applied repeatedly, to create fractal patterns. Often this involves replacing a shape with several smaller versions of the same shape, and then repeating the process for each of the new shapes, recursively. Well know examples are Sierpinski triangles and Koch curves.
  • Strange attractors - this technique typically uses a function that takes an (x, y) coordinate and uses it to calculate a new coordinate (x', y'). This is applied iteratively to created a series of points. The sequence of individual points is often chaotic, but if a large number of points are plotted, a complex pattern emerges. Examples include King's Dream and Tinkerbell.
  • Escape-time fractals - this type of fractal is similar to a strange attractor. Starting from a given point (x, y) in the image space, the function is applied iteratively to test whether it diverges or converges, and the initial point is marked with a colour according to the result. This process is repeated for every point in the image space.