## Fractal Single-Tile Pinwheel

### Info

It is hard to find substitution tilings with dense tile orientations
(like the pinwheel tiling)
that uses a single prototile with
fractal boundary. The fractal version of he pinwheel tiling by
Frank and whittaker uses 13 different prototiles.

An extensive computer search revealed that there are only two substitutions
producing tilings with dense tile orientations using five copies of a
single fractal prototile. Both substitutions use the same prototile.
One substitution is shown here, the other one is obtained by dissecting
the blue two tile patch in the supertile in exactly the opposite way
into two of the tiles.

### Substitution Rule

### Patch