A fractal version of the pinwheel tiling
The pinwheel tilings are a remarkable class of tilings of the plane, and our main goal in this article is to introduce a fractal version of them. We will begin by describing how to construct the pinwheel tilings themselves and by discussing some of the properties that have generated so much interest. After that we will develop the fractal version and discuss some of its properties. Finding this fractile version was an inherently interesting problem, and the solution we found is unusual in the tiling literature.