Recursive Exercises IV: Rep-Tiles

polyomino

P-pentomino

L-triomino

sphinx

level

1

2

3

4

5

opacity

If a polyomino can be divided into

n

congruent copies similar to itself, it is called an

n

-reptile. Rep-tiles are self-similar pieces and so can be regarded as fractals. This Demonstration shows three polyominoes that are 4-reptiles: the P-pentomino, the L-triomino, and the sphinx—which is a polyiamond.

By decreasing opacity, a 3D shape behind shows up; by turning it, you are presented with architectural designs based on these shapes.