http://de.evo-art.org/index.php?action=history&feed=atom&title=Fractal_Tilings_Based_on_Dissections_of_Polyominoes 2026-05-06T00:19:32Z 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_Polyominoes&diff=4148&oldid=prev 2015-01-30T20:29:36Z

<p>Die Seite wurde neu angelegt: „ == Reference == Robert W. Fathauer: <a href="/index.php?title=Fractal_Tilings_Based_on_Dissections_of_Polyominoes" title="Fractal Tilings Based on Dissections of Polyominoes">Fractal Tilings Based on Dissections of Polyominoes</a>. In: <a href="/index.php?title=Bridges_2006" title="Bridges 2006">Bridges 2006</a>. Pages 293–300 == DOI == == Abstract …“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Robert W. Fathauer: [[Fractal Tilings Based on Dissections of Polyominoes]]. In: [[Bridges 2006]]. Pages 293–300 <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-to-<br /> edge fractal tilings. We give examples of fractal tilings with 2-fold and 4-fold rotational symmetry based on<br /> prototiles derived by dissecting polyominoes with 2-fold and 4-fold rotational symmetry, respectively. A<br /> systematic analysis is made of candidate prototiles based on lower-order polyominoes. In some of these fractal<br /> tilings, polyomino-shaped holes occur repeatedly with each new generation. We also give an example of a fractal<br /> knot created by marking such tiles with Celtic-knot-like graphics.<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, Fractal Tilings Based on Dissections of Polyhexes, in Renaissance Banff,<br /> Mathematics, Music, Art, Culture Conference Proceedings, 2005, edited by Reza Sarhangi and Robert V.<br /> Moody, pp. 427-434, 2005.<br /> <br /> [5] Robert W. Fathauer, http://members.cox.net/fractalenc/encyclopedia.html.<br /> <br /> [6] Bruno Ernst, The Magic Mirror of M.C. Escher, Ballantine Books, New York, 1976.<br /> <br /> [7] Peter Raedschelders, “Tilings and Other Unusual Escher-Related Prints,” in M.C. Escher’s Legacy,<br /> edited by Doris Schattschneider and Michele Emmer, Springer-Verlag, Berlin, 2003.<br /> <br /> [8] Branko Grünbaum and G.C. Shephard, Tilings and Patterns, W.H. Freeman, New York, 1987.<br /> <br /> [9] Solomon W. Golomb, Polyominoes, Princeton University Press, Princeton, New Jersey, 1994.<br /> <br /> [10] The only pentomino with 4-fold rotational symmetry yields prototiles with 3 short edges. Adding 4<br /> squares to this pentomino yields prototiles with either 3 or 5 short pseudo-edges. It can easily be seen<br /> that adding four squares to any 4-fold polyomino will either add 2 short pseudo-edges, leave the number<br /> of short pseudo-edges unchanged, or subtract 2 short pseudo-edges. The number of short pseudo-edges<br /> for prototiles is therefore always odd.<br /> <br /> [11] H.-O. Peitgen, H. Jürgens, and D. Saupe, Fractals for the Classroom – Part One, Springer-Verlag,<br /> New York, 1992.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2006/bridges2006-293.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2006/bridges2006-293.html</div>

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