Aperiodic Digraph Fractiles

Part of a tiling by fractalized versions of the Penrose Pentacles.

    In the 1970's,Roger Penrose discovered several types of aperiodic tilings of the plane.  (A tiling is called aperiodic, if no translation maps every tile to another tile.)  It turns out that digraph self-similarity provides a fresh look at his tiles.  You may download a copy of a paper I have written on this topic in PDF format and the notebook which generated the figures for the paper.  You will also need the DigraphFractals package to run the code in the notebook.