Fractal Reptiles Based on Polyforms

A self-replicating tile, or "reptile", is a tile that can be tiled by smaller copies of itself. Polyominoes, polyhexes, and polyiamonds are shapes comprised of squares, hexagons, and equilateral triangles, respectively, joined in edge-to-edge fashion. These polyforms can be arranged in ways that result in fractal reptiles in the limit of an infinite number of iterations. This process is described in detail in a 2025 paper by Robert Fathauer. The method is described more briefly here.

The polyforms shown as buttons below link to pages with fractal reptiles based on them.