Geometry of Self-Contacting Binary Fractal Trees

Benoit Mandelbrot
 and
Michael Frame


Here we present several animations illustrating the constructions of [FT]. We consider binary fractal trees, with branch scaling chosen so some points of the left and right branches intersect, but only at the branch tips. The animations show how the geometry of the tree, and of the branch tips, changes as the branching angle increases.

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