Tom Lowe
TomL@mathstodon.xyz
<p>I'm interested in Computer Graphics, Geometry, Mathematics and Physics. I have worked in Games Development, Animation Development, and now in Robotics Development, I guess that makes me a developer.<br />Vous pouvez me parler dans n'importe quelle langue, c'est assez facile à traduire en ligne si je ne le connais pas.</p>
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The last method needs a tweak, the little green patches do need the transition (dull yellow) tile between them and the larger brown patch. But with that in place it seems to be solidly continuous. Here I&#39;m stress testing it by changing the geometry of the underlying globe limit set. Top is spherical. Middle shrinks the bottom generating sphere to make it cratered. Bottom shrinks another sphere that overlaps the two child sets. So my takeaway is that it&#39;s possible to transition...
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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)
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To make a world-like landscapes with an inversive substitution limit set requires the root limit set to be close to spherical, which you get from having the generating spheres placed on the vertices of a Platonic solid. Last post used an octahedral configuration. This only allows the bumpy tree-tree and cratered shell-shell child sets since the substitution needs to match one sphere and its immediate neighbours (up to a Mobius transformation), leaving only a single sphere for variation. All th...