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

Bobenko, Alexander I.; Hoffmann, Tim

Experiment. Math., Tome 10 (2001) no. 3, p. 141-150 / Harvested from Project Euclid

Résumé

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

Publié le : 2001-05-14
Classification: 52Cxx

@article{999188429,
     author = {Bobenko, Alexander I. and Hoffmann, Tim},
     title = {Conformally Symmetric Circle Packings: A Generalization of Doyle's Spirals},
     journal = {Experiment. Math.},
     volume = {10},
     number = {3},
     year = {2001},
     pages = { 141-150},
     language = {en},
     url = {http://dml.mathdoc.fr/item/999188429}
}

Bobenko, Alexander I.; Hoffmann, Tim. Conformally Symmetric Circle Packings: A Generalization of Doyle's Spirals. Experiment. Math., Tome 10 (2001) no. 3, pp.  141-150. http://gdmltest.u-ga.fr/item/999188429/