Among John Conway's many many mathematical interests is interesting tessellations. Here's a tessellation by inflation and deflation that shares many qualities with Penrose quasiperiodic tessellations. One interesting property is that because of the choice of angles, the original triangle appears in infinitely many orientations in the full plane.
The Wikipedia entry on the Pinwheel Tessellation:
[url]http://en.wikipedia.org/wiki/Pinwheel_tiling[/url]
