Experimental Mathematics

Conformally Symmetric Circle Packings: A Generalization of Doyle's Spirals

Alexander I. Bobenko and Tim Hoffmann


From the geometric study of the elementary cell of hexagonal circle packings---a flower of 7 circles---the class of conformally symmetric circle packings is defined. Up to Möbius transformations, this class is a three parameter family, that contains the famous Doyle spirals as a special case. The solutions are given explicitly. It is shown that these circle packings can be viewed as descretization s of the quotient of two Airy functions. The online version of this paper contains Java applets that let you experiment with the circle packings directly. The applets are found at http://www-sfb288.math.tu-berlin.de/Publications/online/cscpOnline/Applets.html

Article information

Experiment. Math., Volume 10, Issue 1 (2001), 141-150.

First available in Project Euclid: 30 August 2001

Permanent link to this document

Mathematical Reviews number (MathSciNet)
MR1 822 860

Zentralblatt MATH identifier

Primary: 52Cxx: Discrete geometry


Bobenko, Alexander I.; Hoffmann, Tim. Conformally Symmetric Circle Packings: A Generalization of Doyle's Spirals. Experiment. Math. 10 (2001), no. 1, 141--150. https://projecteuclid.org/euclid.em/999188429

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