Doyle Spiral Circle Packings Animated
Inhaltsverzeichnis
Reference
Alan Sutcliffe: Doyle Spiral Circle Packings Animated. In: Bridges 2008. Pages 131–138
DOI
Abstract
Doyle spiral circle packings are described. Two such packings illustrate some of the properties of the packings in general, with some of the mathematics needed for their construction. Each of these two packings is the basis for a short animation. The first uses self-similarity to make endless zooms by repetition of a short sequence. The second animation is composed of short sections using the circle packing in different decorative forms. A visual aid to approximation is described.
Extended Abstract
Bibtex
Used References
[1] Dov Aharonov and Kenneth Stephenson, Geometric Sequences in Discs in the Apollonian Packing, Algebra i Analiz, 9, 3, 1997, pp 104 – 140.
[2] Alan Beardon, Tomasz Dubejko and Kenneth Stephenson, Spiral Hexagonal Circle Packings in the Plane, Geometriae Dedicata, 49, 1994, pp 39 – 70.
[3] A. L. Bobenko and Tim Hoffman, Conformally Symmetric Circle Packings: a Generalization of Doyle’s Spirals, Experimental Mathematics, 10, 2001, pp 141 – 150.
[4] Peter Doyle, He Zheng-Zu and Burt Rodin, Second Derivatives and Estimates for Hexagonal Circle Packing, Discrete Computational Geometry, 11, 1994, pp 35 - 49.
[5] Kenneth Stephenson, Introduction to Circle Packing, Cambridge University Press, 2005.
[6] Ron Weeden, Hexlets and Doyle Spirals and other unpublished papers, revised 2007.
Links
Full Text
http://archive.bridgesmathart.org/2008/bridges2008-131.pdf
