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If you enjoyed learning about the Hashlife algorithm for Conway's Game of Life, the bilinear approximation algorithm for computing whether a point is in the man
by QuadmasterXLII 3y ago
If you enjoyed learning about the Hashlife algorithm for Conway's Game of Life, the bilinear approximation algorithm for computing whether a point is in the mandelbrot set has the same je ne sais quoi. No one has done a really accessible writeup of it yet, but this blog post and the linked forum thread are a good start: https://mathr.co.uk/blog/2022-02-21_deep_zoom_theory_and_practice_again.html#a2022-02-21_deep_zoom_theory_and_practice_again_bilinear_approximation https://mathr.co.uk/blog/2022-02-21_deep_zoom_theory_and_pra...
- RBerenguel 3y agoI did some research on this on the side for my dissertation, but never published it. The fact centers approximate the boundary generalises to almost any point in the plane as a consequence of normality of some sequences, and generalises to most families of complex iteration under very mild conditions. I’ve had a preprint that I never felt like finishing for something like 15 years lying around.
- QuadmasterXLII 3y agoIf you ever decide to put it out as-is, I'd love to read it!
- RBerenguel 3y agoI should probably brush it up and just upload it to Arxiv. But then I need ok from my advisor, and maybe she’d rather not (since she’d be a coauthor of that..). I’ll try again, thanks for the encouragement.