Platonic solid fractals and their complements

Written by Paul Bourke
Inspired by Gayla Chandler

December 2005

Illustrated here are fractals created using each of the platonic solids. Except for the special case of the cube, each fractal is created by positioning reduced versions of the platonic solid along the line from the center to each vertex of the solid. The exact reduction and the distance along the line is chosen so the final form is connected and the overall shape is the same as the seeding platonic solid. This procedure fails to give anything interesting for the cube so the Menger sponge is used instead. In addition the complement of each fractal is shown (in blue), that is, the fractal subtracted from the original platonic solid. The POVRay files are given for each form, render them with integer clock values from 0 upwards, the even numbered frames are the fractals, the odd numbered frames are the complements.

Tetrahedron