Chaos and Fractals#

To show the possible speedups for numerical Python code, we use a very ideal example for computation belonging to the area of chaos and fractals.

Chaos in the scientific sense mainly stands for unpredictable behaviour in systems. Think of the Butterfly Effect. A very theoretical example for sure.

Fractals on the other hand show very complex patterns and shapes, very similar to natural structures, which can be produced by simple mathematical formulas and algorithms.

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Fig. 4 Junger Wurmfarn, Photo taken by Mabit1, CC BY-SA 4.0#

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Fig. 5 Romanesco, Photo taken by Wolfgang Beyer, CC BY-SA 3.0#

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Fig. 6 Dragon Curve#

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Fig. 7 Fractal Tree#

We’re looking at a very special fractal today, the Mandelbrot Set.