Fractal Tilings Based on Dissections of Polyominoes

Robert W. Fathauer
Bridges London: Mathematics, Music, Art, Architecture, Culture (2006)
Pages 293–300


Polyominoes, shapes made up of squares connected edge-to-edge, provide a rich source of prototiles for edge-to-edge 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.