Creating repeating hyperbolic patterns
Creating repeating hyperbolic patterns
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DOI：
10.1145/800224.806808
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发表时间：
1981-08
期刊：
影响因子：
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通讯作者：
Douglas Dunham;J. Lindgren;D. Morris
中科院分区：
文献类型：
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作者：
Douglas Dunham;J. Lindgren;D. Morris
描述了用于创建双曲线平面的重复图案的过程。与欧几里德平面不同，双曲平面有无穷多种不同的重复模式。双曲几何的庞加莱圆模型已经被艺术家M。C.显示联锁，重复，双曲线模式的显示器。已经设计了一个程序，它将自动完成这项工作。用户输入一个主题或基本子图案，理论上可以复制以填充双曲线平面。在实践中，复制过程可以足够频繁地迭代，以填充圆模型。有一个互动的“边界程序”，允许用户设计一个主题，将被复制成一个完全联锁的模式。文中包括两种仿布氏模式和一些全新的模式。
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.