Fractal Tilings Based on Dissections of Polyominoes

Polyominoes, shapes made up of squares connected edge-to-edge, provide a rich source of prototiles for edge-toedge fractal tilings. We give examples of fractal tilings with 2-fold and 4-fold rotational symmetry based on prototiles derived by dissecting polyominoes with 2-fold and 4-fold rotational symmetry, respectively. A systematic analysis is made of candidate prototiles based on lower-order polyominoes. In some of these fractal tilings, polyomino-shaped holes occur repeatedly with each new generation. We also give an example of a fractal knot created by marking such tiles with Celtic-knot-like graphics.