A Self-Tiling Tile Set

Futility Closet recently posted about a recursive set of tiles from Lee Sallows. It describes 9 shapes that are defined by different arrangements of a roughly Utah shaped piece. They can be combined into three identical shapes that are 3 times larger than the base pieces.

One interesting thing I found, that wasn’t described in the post, is that all three final pieces are composed of the same arrangement of the smallest pieces.

This image shows the same tiling with the smallest tiles outlined and the colors removed, showing that the layout is identical. You could make your own set of nine tiles, different than the original, by coloring in groups of three on this template.