Fractal tilings in the plane

Fractiles are tiles bounded by fractal curves. They may be generated using an iterative procedure, whereby at least two functions are repeatedly composed. The functions are formed from translates of the inverse of a linear transformation of the form g(z) = Mz, in which M is an invertible 2x2 matrix having integer entries. The inverse transformation g-1(z) is then responsible for mapping the whole fractal tiling onto a fractile.