Fractal with Barycentric Coordinates

This fractal idea did not originate with me, but I wrote some racket code to do the midpoint calculation using barycentric coordinates. This fractal draws a circle at the midpoint of a triangle, then subdivides the triangle and repeats:

Here is the same fractal to four iterations:

To get the midpoints, I could simple pass in the coordinates of the last triangle ABC, and then use “0.5” barycentric coordinates:

        [P1 (barycentric->complex 0.5 0.5 0 A B C)]
        [P2 (barycentric->complex 0.5 0.0 0.5 A B C)]
        [P3 (barycentric->complex 0 0.5 0.5 A B C)]

Here is the full code:

ftp://lavender.qlfiles.net/Racket/bc-fractal.7z

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