http://de.evo-art.org/index.php?action=history&feed=atom&title=Fractal_tilings_based_on_dissections_of_polyhexes 2026-04-14T19:54:55Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Fractal_tilings_based_on_dissections_of_polyhexes&diff=911&oldid=prev 2014-11-03T20:57:43Z

<p>Die Seite wurde neu angelegt: „ == Reference == Fathaner, R.: Fractal tilings based on dissections of polyhexes. In: Bridges Proceedings 2005, pp. 427–434 (2005). == DOI == == Abstract…“</p> <p><b>Neue Seite</b></p><div> <br /> <br /> == Reference ==<br /> Fathaner, R.: Fractal tilings based on dissections of polyhexes. In: Bridges Proceedings 2005, pp. 427–434 (2005).<br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> 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.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] Robert W. Fathauer, Fractal tilings based on kite- and dart-shaped prototiles, Computers &amp; Graphics,<br /> Vol. 25, pp. 323-331, 2001.<br /> <br /> [2] Robert W. Fathauer, Fractal tilings based on v-shaped prototiles, Computers &amp; Graphics, Vol. 26, pp.<br /> 635-643, 2002.<br /> <br /> [3] Robert W. Fathauer, Self-similar Tilings Based on Prototiles Constructed from Segments of Regular<br /> Polygons, in Proceedings of the 2000 Bridges Conference, edited by Reza Sarhangi, pp. 285-292, 2000.<br /> <br /> [4] Robert W. Fathauer, http://members.cox.net/fractalenc/encyclopedia.html. 404<br /> <br /> [5] Bruno Ernst, The Magic Mirror of M.C. Escher, Ballantine Books, New York, 1976.<br /> <br /> [6] F.H. Bool, J.R. Kist, J.L. Locher, and F. Wierda, M.C. Escher – His Life and Complete Graphic Work,<br /> Abrams, New York, 1982.<br /> <br /> [7] Branko Grünbaum and G.C. Shephard, Tilings and Patterns, W.H. Freeman, New York, 1987.<br /> <br /> [8] H.-O. Peitgen, H. Jürgens, and D. Saupe, Fractals for the Classroom – Part One, Springer-Verlag,<br /> New York, 1992.<br /> <br /> [9] This puzzle, known as HexaPlex, may be seen at http://www.tessellations.com.<br /> <br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://www.mathartfun.com/shopsite_sc/store/html/Compendium/Bridges2005.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.4211</div>

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