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.

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