The base pattern is a selfsimilar tiling obtained by iteratively trisecting the triangles into 3 smaller copies.
I then Identify the small triangles with 3-adic integers: The nth digit tells which triangle to take in the nth iteration.
The metric on the 3-adic numbers d(x,y)=3^(-n) where n the smallest place where their digits differ.
This is a Voronoi complex to a growing point set. I randomly add new numbers and let their cell grow to encompass all numbers closer to them than any coming before.
Black is the boundary: numbers that are closest to two or more of the numbers I chose.
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