Creating repeating hyperbolic patterns

Association for Computing Machinery (ACM) - Tập 15 Số 3 - Trang 215-223 - 1981
Douglas Dunham1, John A. Lindgren1, David Witte2
1Department of Mathematical Sciences, University of Minnesota, Duluth, Duluth, MN
2Department of Mathematics, University of Chicago, Chicago, IL

Tóm tắt

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.

Từ khóa


Tài liệu tham khảo

Alexander H., 1978, Realized by Means of Computer plus Plotter

Coxeter H.S.M., 1957, Trans. Royal Soc. Canada (3), 51, 1

Coxeter H. S.M., 1961, Introduction to Geometry, 2

10.1007/978-3-662-25739-5

Fricke R., 1890, Vorlesungen uber die Theorie der elliptischen Modulfunktionen

Locher J. L., 1971, The World of M. C. Escher

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Thông tin xuất bản

Association for Computing Machinery (ACM)

Tập 15 Số 3

215-223

Thông tin tác giả