Fractal Tilings Based on Dissections of Polyhexes

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Robert W. Fathauer: Fractal Tilings Based on Dissections of Polyhexes. In: Bridges 2005. Pages 427–434



Polyhexes, shapes made up of regular hexagons connected edge-to-edge, provide a rich source of prototiles for edge-to-edge fractal tilings. Numerous examples are given of fractal tilings with 2-fold and 3-fold rotational symmetry based on prototiles derived by dissecting polyhexes with 2-fold and 3-fold rotational symmetry, respectively. A systematic analysis is made of candidate prototiles based on lower-order polyhexes.

Extended Abstract


Used References

[1] Robert W. Fathauer, Fractal tilings based on kite- and dart-shaped prototiles, Computers & Graphics, Vol. 25, pp. 323-331, 2001.

[2] Robert W. Fathauer, Fractal tilings based on v-shaped prototiles, Computers & Graphics, Vol. 26, pp. 635-643, 2002.

[3] Robert W. Fathauer, Self-similar Tilings Based on Prototiles Constructed from Segments of Regular Polygons, in Proceedings of the 2000 Bridges Conference, edited by Reza Sarhangi, pp. 285-292, 2000.

[4] Robert W. Fathauer,

[5] Bruno Ernst, The Magic Mirror of M.C. Escher, Ballantine Books, New York, 1976.

[6] F.H. Bool, J.R. Kist, J.L. Locher, and F. Wierda, M.C. Escher – His Life and Complete Graphic Work, Abrams, New York, 1982.

[7] Branko Grünbaum and G.C. Shephard, Tilings and Patterns, W.H. Freeman, New York, 1987.

[8] H.-O. Peitgen, H. Jürgens, and D. Saupe, Fractals for the Classroom – Part One, Springer-Verlag, New York, 1992.

[9] This puzzle, known as HexaPlex, may be seen at


Full Text

intern file

Sonstige Links