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  • Adam Goucher
  • Dave Greene

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2012 September 11

The Mandelbrot set in HighLife

As detailed over on Complex Projective 4-Space, I computed some large images of the Mandelbrot set. For example, here is part of a screenshot of Golly, looking at the Seahorse Valley in the Mandelbrot set:

2012-09-11-seahorse.PNG

With Golly, we can run the Mandelbrot set in a cellular automaton. The results are fairly uninteresting with B3/S23, so I simulated the boundary (obtained from the original image by one generation of B3/S23) in HighLife (B36/S23) instead. As with all sufficiently large chaotic HighLife universes, profusions of replicators emerge:

2012-09-11-mset-b36s23.PNG

You can download the files from Complex Projective 4-Space yourself if you're interested in running a simulation. For these purposes, you'll want the 262144 by 262144 monochromatic image (25 MB download as .mc.gz), rather than the scaled-down colourful version.

In both HighLife and ordinary Life, we obtain four waves of gliders, a handful of orthogonal spaceships and a few diamonds on the real axis. These diamonds are caused by long unbroken lines expanding. In Life, we get two back-to-back Sierpinski triangles, compared with a uniform pattern of blinkers in HighLife. Further, these blinkers are very vulnerable to chaos, resulting in the destruction apparent in the green-bordered inset image.