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Author Witte, David ♦ Lindgren, John ♦ Dunham, Douglas
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Hyperbolic geometry ♦ Poincare circle model ♦ M. c. escher ♦ Computer art ♦ Tessellations ♦ Repeating pattern ♦ Symmetry groups ♦ Motif ♦ Interactive graphics
Abstract A process for creating repeating patterns of the hyperbolic plane is described. Unlike the Euclidean plane, the hyperbolic plane has infinitely many different kinds of repeating patterns. The Poincare circle model of hyperbolic geometry has been used by the artist M. C. Escher to display interlocking, repeating, hyperbolic patterns. A program has been designed which will do this automatically. The user enters a motif, or basic subpattern, which could theoretically be replicated to fill the hyperbolic plane. In practice, the replication process can be iterated sufficiently often to appear to fill the circle model. There is an interactive “boundary procedure” which allows the user to design a motif Which will be replicated into a completely interlocking pattern. Duplication of two of Escher's patterns and some entirely new patterns are included in the paper.
Description Affiliation: Department of Mathematical Sciences, University of Minnesota, Duluth, Duluth, MN (Dunham, Douglas; Lindgren, John) || Department of Mathematics, University of Chicago, Chicago, IL (Witte, David)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1988-08-01
Publisher Place New York
Journal ACM SIGGRAPH Computer Graphics (COMG)
Volume Number 15
Issue Number 3
Page Count 9
Starting Page 215
Ending Page 223


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Source: ACM Digital Library