## Fractal with Barycentric Coordinates Variations

One can generate a few slight variations on the appearance of the previous fractal by altering the scaling factoring of the circle radius a little:

It is interesting also that this fractal draws in such a way that you can paint alternate cells without painted cells touching each other: I.e., they only touch at the vertices.

## 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