http://de.evo-art.org/index.php?action=history&feed=atom&title=Two-color_Fractal_Tilings 2026-04-18T13:44:49Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Two-color_Fractal_Tilings&diff=3976&oldid=prev 2015-01-28T20:47:31Z

<p>Die Seite wurde neu angelegt: „ == Reference == Robert W. Fathauer: <a href="/index.php?title=Two-color_Fractal_Tilings" title="Two-color Fractal Tilings">Two-color Fractal Tilings</a>. In: <a href="/index.php?title=Bridges_2012" title="Bridges 2012">Bridges 2012</a>. Pages 199–206 == DOI == == Abstract == A variety of two-color f…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Robert W. Fathauer: [[Two-color Fractal Tilings]]. In: [[Bridges 2012]]. Pages 199–206 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> A variety of two-color fractal tilings (f-tilings) are described, in which no two adjacent tiles have the same color.<br /> Two-colorable examples from f-tilings that have been described previously are identified, and two techniques are<br /> used for converting f-tilings that are not two-colorable into new f-tilings that can be so colored. In the first of<br /> these, tiles are combined in order to change the valence of vertices to all be even, ensuring two-colorability. This<br /> technique is applicable to a limited number of f-tilings and can result in prototiles with an infinite number of edges<br /> and corners. In the second technique, tiles are divided into two or more smaller tiles such that all vertices of the<br /> new f-tiling have even valence.<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;<br /> Graphics, Vol. 25, pp. 323-331, 2001.<br /> <br /> [2] Robert W. Fathauer, Fractal tilings based on v-shaped prototiles, Computers &amp; Graphics, Vol. 26,<br /> pp. 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,<br /> 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<br /> Robert V. Moody, pp. 427-434, 2005.<br /> <br /> [5] Robert W. Fathauer, Fractal Tilings Based on Dissections of Polyominoes, in Bridges London,<br /> Mathematics, Music, Art, Architecture, Culture Conference Proceedings, 2006, edited by Reza<br /> Sarhangi and John Sharp, pp. 293-300, 2006.<br /> <br /> [7] Robert W. Fathauer, http://www.mathartfun.com/shopsite_sc/store/html/Compendium/encyclopedia.html.<br /> <br /> [6] Robert W. Fathauer, “Fractal Tilings Based on Dissections,” in Homage to a Pied Piper, edited by<br /> Ed Pegg Jr., Alan Schoen, and Tom Rodgers, AK Peters, Wellesley, MA, 2009.<br /> <br /> [8] Bruno Ernst, The Magic Mirror of M.C. Escher, Ballantine Books, New York, 1976.<br /> <br /> [9] 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 /> [10] K.W. Chung and H.M. Ma, Automatic generation of aesthetic patterns on fractal tilings by means of<br /> dynamical systems,” Chaos, Solitons, and Fractals, Vol. 24, pp. 1145-1158, 2005.<br /> <br /> [11] Branko Grünbaum and G.C. Shephard, Tilings and Patterns, W.H. Freeman, New York, 1987.<br /> <br /> [12] König, D., Theorie der endlichen und unendlichen Graphen, Leipzig, 1936.<br /> <br /> [13] Robert W. Fathauer, unpublished.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2012/bridges2012-199.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2012/bridges2012-199.html</div>

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