Generalizations
Radin and Conway proposed a three dimensional analogue which was dubbed the quaquaversal tiling. There are other variants and generalizations of the original idea.
One gets a fractal by iteratively dividing in five isometrics copies, following the Conway construction, and discarding the middle triangle (ad infinitum). This Pinwheel fractal has Hausdorff dimension .
Read more about this topic: Pinwheel Tiling