Circle packing with generalized branching

Edward T Crane, Kenneth Stephenson, James Ashe

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Attempts to build a discrete theory for rational maps on the sphere via circle packing have foundered on discretization effects in locating branch points. The authors remove this impediment by introducing generalized branch points. A generalized branch point need no longer be attached to an individual circle, but with the help of chaperones and other devices, can be positioned anywhere that the geometry requires. The effects are illustrated in images and videos as we use generalized branching to fix flaws in discrete Ahlfors and Weierstrass functions.
Original languageEnglish
Pages (from-to)251–276
Number of pages28
JournalJournal of Analysis
Issue number2
Early online date8 Dec 2016
Publication statusPublished - Dec 2016


  • Circle packing
  • Discrete analytic function
  • Blaschke product
  • Ahlfors function
  • Branch point

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