Generating repeating hyperbolic patterns based on regular tessellations using an applet

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Generating repeating hyperbolic patterns based on regular tessellations using an applet

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2013-12

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Some of the hyperbolic patterns of the Dutch artist M. C. Escher, which are considered as the finest works of hyperbolic geometry art, are computer-generated using algorithms that create hyperbolic patterns by replicating a basic sub-pattern called the motif. Escher created his patterns by hand - a very tedious and time consuming task. This paper describes the creation of these patterns using a computer program. The current algorithms that generate these repeating patterns are based on the regular tessellation of the hyperbolic plane, {p, q}, where "p" denotes a regular p-sided polygon, and "q" specifies the number of them that meet at each vertex. The focus of this research is to replicate these patterns using a Java applet, which makes the program portable across the platforms. The applet loads a data file that contains the information to generate a repeating pattern for the external user. The user can also create and modify such a data file using the user interface of the applet. The patterns generated are displayed on the screen quickly and precisely. The research uses Weierstrass Model of Hyperbolic Geometry for all calculations and Poincaré's model of Hyperbolic Geometry as the basis for representations of the desired patterns.

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University of Minnesota M.S. thesis. December 2013. Major: Computer science. Advisor: Douglas J. Dunham. 1 computer file (PDF); v, 78 pages.

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Vejendla, Maneesha. (2013). Generating repeating hyperbolic patterns based on regular tessellations using an applet. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/162408.

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