Post #2454886
2026-05-08 18:57 UTC
@csk@mathstodon.xyz Nice to see this implemented, Craig.
I'm curious how you determine which fractal shape, if any, a control point lies in. Is it anything like the iterative process I describe here: https://mathstodon.xyz/@pieter/115951754157537975?
Replies (1)
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@csk@mathstodon.xyz 2026-05-08 19:33
@pieter@mathstodon.xyz I think I went through a very similar train of thought. Selinger's construction ultimately produces the fractal as a union of disjoint triangles, and you can iteratively descend through levels of substitution, bailing out early if you ever reach a "definitely inside" or "definitely outside" sub-region. But I boringly iterate over ever smaller quadrilaterals, rather than inverse-transforming the sample point relative to fixed shapes (I agree that both directions will probably work fine).