Fractal tilings based on dissections of polyhexes
Inhaltsverzeichnis
Reference
Fathaner, R.: Fractal tilings based on dissections of polyhexes. In: Bridges Proceedings 2005, pp. 427–434 (2005).
DOI
Abstract
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. 1.
Extended Abstract
Bibtex
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, http://members.cox.net/fractalenc/encyclopedia.html. 404
[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 http://www.tessellations.com.
Links
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http://www.mathartfun.com/shopsite_sc/store/html/Compendium/Bridges2005.pdf
Sonstige Links
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.4211
