http://de.evo-art.org/index.php?action=history&feed=atom&title=Some_Hyperbolic_Fractal_Tilings 2026-04-20T13:32:35Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Some_Hyperbolic_Fractal_Tilings&diff=3831&oldid=prev 2015-01-27T13:43:33Z

<p>Die Seite wurde neu angelegt: „ == Reference == Robert W. Fathauer: <a href="/index.php?title=Some_Hyperbolic_Fractal_Tilings" title="Some Hyperbolic Fractal Tilings">Some Hyperbolic Fractal Tilings</a>. In: <a href="/index.php?title=Bridges_2014" title="Bridges 2014">Bridges 2014</a>. Pages 87–94 == DOI == == Abstract == The concepts of frac…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Robert W. Fathauer: [[Some Hyperbolic Fractal Tilings]]. In: [[Bridges 2014]]. Pages 87–94 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> The concepts of fractal tiling and hyperbolic tiling are combined to create novel fractal surfaces in Euclidean three-<br /> space. Paper folding and computer modeling are used to create these constructs. We show examples using triangular,<br /> trapezoidal, and dart-shaped prototiles. Smaller tiles deflect out of the plane of adjacent larger tiles, resulting in non-<br /> planar surfaces, the shapes of which are dependent on the rules governing the sign of the deflections as well as their<br /> magnitudes. These constructs are an intriguing blend of organic and geometric character and in some cases bear<br /> marked resemblance to natural leaves.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] John H. Conway, Heidi Burgiel, and Chaim Goodman-Strauss, The Symmetries of Things, A K<br /> Peters, Ltd., Wellesley, MA, 2008.<br /> <br /> [2] Robert W. Fathauer, Fractal tilings based on kite- and dart-shaped prototiles, Computers &amp;<br /> Graphics, Vol. 25, pp. 323-331, 2001.<br /> <br /> [3] Robert W. Fathauer, Fractal Tilings Based on Dissections of Polyominoes, Polyhexes, and<br /> Polyiamonds, in Homage to a Pied Puzzler, ed. by Ed Pegg, Jr., Alan H. Schoen, and Tom Rodgers,<br /> A K Peters, Ltd., Wellesley, MA, 2009.<br /> <br /> [4] Edmund Harriss, Maxwell’s Demon website, http://maxwelldemon.com/2009/04/13/unscheduled-post-hyperbolic-polydron/, accessed February 5, 2014.<br /> <br /> [5] Geoffrey Irving and Henry Segerman, Developing fractal curves, J. of Mathematics and the Arts,<br /> Vol. 7, pp. 103-121, 2013.<br /> <br /> [6] Peichang Ouyang and Robert Fathauer, Aesthetic Patterns Based on Fractal Tilings, IEEE<br /> Computer Graphics, Vol. 34, pp 68-76, 2014.<br /> <br /> [7] Hans-Otto Peitgen, Hartmut Jürgens, and Dietmar Saupe, Fractals for the Classroom, Springer-<br /> Verlag, New York, 1992.3<br /> <br /> [8] Przemyslaw Prusinkiewicz and Pierre Barbier de Reuille, Constraints of Space in Plant<br /> Development, J. of Experimental Botany, Vol. 61, pp. 2117-2129, 2010.<br /> <br /> [9] Daina Taimina, Crocheting Adventures with Hyperbolic Planes, A K Peters, Ltd., Wellesley, MA,<br /> 2009.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2014/bridges2014-87.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2014/bridges2014-87.html</div>

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