Escape-time fractals in generativepy

Martin McBride
2021-12-16

Escape time fractals are similar to strange attractors.

Starting from a given point (x, y) in the image space, the function is applied iteratively to test whether it diverges or converges. The initial point is marked with a colour according to the result.

This process is repeated for every point in the image space. By the end, every pixel in the image is marked with a colour to indicate whether the iteration starting at that point will diverge or converge.

In some cases, the colour of the pixel is changed to indicate how many iterations were required for the values to diverge beyond some arbitrary point. This can reveal more details of the fractal.

Comparison with strange attractors

The key difference between strange attractors and escape-time fractals is:

  • For a strange attractor, starting from a single point (x, y) we use the formulae to generate a sequence of other points that are marked as being part of the attractor.
  • For an escape-time fractal, for every point (x, y) in the image, we apply the formula repeatedly and test whether it diverges or converges, and mark that pixel accordingly.

Here are some escape-time fractals:

See also

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