Creating repeating hyperbolic patterns based on regular tessellations.

Abstract

Repeating patterns have been used in art throughout history. In the middle of the 20th century, the noted Dutch artist M.C. Escher was the first to create repeating hyperbolic patterns that were artistic in nature. These patterns were very tedious to design and draw. Escher did all this work by hand, without the benefit of a computer. This paper discusses how, through the use of a computer program, the creation of repeating hyperbolic patterns is accomplished in a less tedious, more timely manner. The computer program enables a user to load or create a data file that defines the sub-pattern and other information about the design. The program will take that information and generate the repeating pattern for the user. The user is also able to modify the pattern. The computer program allows the user to precisely and quickly create repeating hyperbolic patterns which will be displayed on the screen. The repeating hyperbolic pattern is also saved as a PostScript file.