http://de.evo-art.org/index.php?action=history&feed=atom&title=Unfolding_Symmetric_Fractal_Trees 2026-05-17T16:45:04Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Unfolding_Symmetric_Fractal_Trees&diff=3922&oldid=prev 2015-01-28T14:35:22Z

<p>Die Seite wurde neu angelegt: „ == Reference == Bernat Espigulé Pons: <a href="/index.php?title=Unfolding_Symmetric_Fractal_Trees" title="Unfolding Symmetric Fractal Trees">Unfolding Symmetric Fractal Trees</a>. In: <a href="/index.php?title=Bridges_2013" title="Bridges 2013">Bridges 2013</a>. Pages 295–302 == DOI == == Abstract == This work sho…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Bernat Espigulé Pons: [[Unfolding Symmetric Fractal Trees]]. In: [[Bridges 2013]]. Pages 295–302 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> This work shows how the angles and ratios of side to diagonal in the regular polygons generate interesting nested<br /> motifs by branching a canonical trunk recursively. The resulting fractal trees add new material to the theory of<br /> proportions, and may prove useful to other fields such as tessellations, knots and graphs. I call these families of<br /> symmetric fractal trees harmonic fractal trees because their limiting elements, i.e., when the polygon is a circle,<br /> have the overtones or harmonics of a vibrating string 1/2, 1/3, 1/4, ... as their scaling branch ratios. The term<br /> harmonic is also used here to distinguish them from other types of self-contacting symmetric fractal trees that don’t<br /> have a constantly connected tip set under a three-dimensional unfolding process. Binary harmonic trees represent<br /> well-known L ́evy and Koch curves, while higher-order harmonic trees provide new families of generalized fractal<br /> curves. The maps of the harmonic fractal trees are provided as well as the underlying parametric equations.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] B. Espigul ́e. Fractal Trees Project. http://pille.iwr.uni-heidelberg.de/~fractaltree01/.<br /> <br /> [2] R. W. Fathauer. Compendium of Fractal Knots. http://www.mathartfun.com/shopsite_sc/store/html/FractalKnots/ (as of Jan. 26, 2013).<br /> <br /> [3] R. W. Fathauer. Compendium of Fractal Tilings. http://www.mathartfun.com/shopsite_sc/store/html/Compendium/encyclopedia.html (as of Jan. 26, 2013).<br /> <br /> [4] R. 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, pages 285–292, 2000.<br /> <br /> [5] Heinz G ̈otze. Friedrich II and the love of geometry. The Mathematical Intelligencer, 17(4):48–57, 1995.<br /> <br /> [6] Tam ́as Keleti and Elliot Paquette. The Trouble with von Koch Curves Built from n-gons. The American Mathematical Monthly, 117(2):124–137, 2010.<br /> <br /> [7] P. L ́evy. Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole (1938). Classics on Fractals by Gerald A. Edgar, pages 180–239, 2003.<br /> <br /> [8] B.B. Mandelbrot and M. Frame. The Canopy and Shortest Path in a Self-Contacting Fractal Tree. The Mathematical Intelligencer, 21(2):18–27, 1999.<br /> <br /> [9] T. D. Taylor. Golden Fractal Trees. In Proceedings of the 2007 Bridges Conference, edited by Reza Sarhangi and Javier Barallo, pages 181–188, 2007.<br /> <br /> [10] S. Wolfram. A New Kind of Science. Wolfram Media, 2002. http://www.wolframscience.com/nksonline/section-8.6 (as of Jan. 26, 2013).<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2013/bridges2013-295.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2013/bridges2013-295.html</div>

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