Year: 2019
Type: preprint
Abstract: We introduce orthogonal ring patterns consisting of pairs of concentric circles generalizing circle patterns. We show that orthogonal ring patterns are governed by the same equation as circle patterns. For every ring pattern there exists a one parameter family of patterns that interpolates between a circle pattern and its dual. We construct ring pattern analogues of the Doyle spiral, Erf and $z^α$ functions. We also derive a variational principle and compute ring patterns based on Dirichlet and Neumann boundary conditions.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388032122