Post #1580543
2026-04-22 11:44 UTC
There are a couple of problems with the previous substitution rules (post: https://mathstodon.xyz/@TomL/116374713539850562).
The first is that the substituted sets are solidly that one set, which looks unnatural. That can be fixed by having one of the spheres of the child set substitute back in the parent set. So for instance you don't just get patches of vegetation in your bare soil, but also patches of bare soil within your vegetation.
Here the hilly green terrain substitutes back in the parent terrain on one of its 12 spheres:
(1/4)
Replies (1)
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@TomL@mathstodon.xyz 2026-04-22 11:50
This image shows what's happening with the substitutions. The top sphere of the parent set (left) substitutes in the green (right) set, and the top sphere of the green set (right) substitutes in the golden coloured parent set (left). It is of course that large bottom green sphere that makes the green limit set so hilly. Variations include substituting a different child sphere, or a grandchild sphere, or substituting in a third set. (2/4)