http://de.evo-art.org/index.php?action=history&feed=atom&title=Sinuous_Meander_Patterns_in_Natural_Coordinates 2026-04-07T01:18:12Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Sinuous_Meander_Patterns_in_Natural_Coordinates&diff=3975&oldid=prev 2015-01-28T20:44:30Z

<p>Die Seite wurde neu angelegt: „ == Reference == David Chappell: <a href="/index.php?title=Sinuous_Meander_Patterns_in_Natural_Coordinates" title="Sinuous Meander Patterns in Natural Coordinates">Sinuous Meander Patterns in Natural Coordinates</a>. In: <a href="/index.php?title=Bridges_2012" title="Bridges 2012">Bridges 2012</a>. Pages 183–190 == DOI == == Abstract == Natura…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> David Chappell: [[Sinuous Meander Patterns in Natural Coordinates]]. In: [[Bridges 2012]]. Pages 183–190 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> Natural (or intrinsic) coordinate systems parameterize curves based on their inherent properties such as arc length<br /> and tangential angle, independent of external reference frames. They provide a convenient means of representing<br /> many organic, flowing curves such as the meandering of streams and ocean currents. However, even simple<br /> functions written in natural coordinates can produce surprisingly complex spatial patterns that are difficult to<br /> predict from the original generating functions. This paper explores multi-frequency, sine-generated patterns in<br /> which the tangential angle of the curve is related to the curve’s arc length through a series of sine functions. The<br /> resulting designs exhibit repeating forms that can vary in subtle or dramatic ways along the curve depending on the<br /> choice of parameter values. The richness of the “pattern space” of this equation suggests that it and other simple<br /> natural equations might provide fertile ground for generating geometric, organic and even whimsical patterns.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] C. Bier, Symmetry and Symmetry-Breaking An Approach to Understanding Beauty, Bridges 2005<br /> Symposium Proceedings, pp. 219-226, 2005.<br /> <br /> [2] J. A. Staab, Katherine Westphal and Wearable Art, Textile Society of America 2004 Symposium<br /> Proceedings, Ed. C. Bier, pp. 227-233 (CD-ROM), OmniPress, 2005.<br /> <br /> [3] “Fort Yukon, Alaska.” Map, Google Maps, Web, 7 January 2012.<br /> <br /> [4] W. Whewell, Of the Intrinsic Equation of a Curve, and its Application, Transactions of the Cambridge<br /> Philosophical Society, 8, pp. 659-671, 1849.<br /> <br /> [5] L. B. Leopold and W. B. Langbein, River Meanders, Scientific American, 214, pp. 60-70, June 1966.<br /> <br /> [6] B. Hayes, Up a Lazy River, American Scientist, 94, pp. 490-4, 2006.<br /> <br /> [7] P. Gailiunas, Meanders, Bridges 2005 Symposium Proceedings, pp 25-31, 2005.<br /> <br /> [8] N. Movshovitz-Hadar and A. Shmukler, River Meandering and a Mathematical Model of this<br /> Phenomenon, Physica Plus, physicaplus.org.il, issue 7, 2006.<br /> <br /> [9] C.G. Fraser, Mathematical technique and physical conception in Euler’s investigation of the Elastica,<br /> Centaurus, 34, pp. 211-246, 1991.<br /> <br /> [10] R. L. Levien, From Spiral to Spline: Optimal Techniques in Interactive Curve Design, Ph.D. thesis,<br /> University of California, Berkeley, 2009.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2012/bridges2012-183.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2012/bridges2012-183.html</div>

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