Conformal tilings I: foundations, theory, and practice

conformal tilings. These are similar to traditional tilings in that they realize abstract patterns of combinatorial polygons as concrete patterns of geometric shapes, the tiles. In the conformal case, however, these geometric tiles carry prescribed conformal rather than prescribed euclidean structur...

Full description

Saved in:
Bibliographic Details
Published in:Conformal geometry and dynamics 2017-01, Vol.21 (1), p.1-63
Main Authors: Bowers, Philip, Stephenson, Kenneth
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:conformal tilings. These are similar to traditional tilings in that they realize abstract patterns of combinatorial polygons as concrete patterns of geometric shapes, the tiles. In the conformal case, however, these geometric tiles carry prescribed conformal rather than prescribed euclidean structure. The authors develop the topic from the ground up: definitions and terminology, basic theory on existence, uniqueness and properties, numerous experiments and examples, comparisons to traditional tilings, patterns unique to conformal tiling, and details on computability through circle packing. Special attention is placed on aperiodic hierarchical tilings and on connections between abstract combinatorics on one hand and their geometric realizations on the other. Many of the motivations for studying tilings remain unchanged, not least being the pure beauty and intricacy of the patterns.]]>
ISSN:1088-4173
1088-4173
DOI:10.1090/ecgd/304