An Interactive Java Program to Generate Hyperbolic

Abstract

Artists have created various repeating patterns and they have been absorbed into various cultures across the world as art. Notable are the works of the Dutch artist M.C. Escher who was most likely the first to create such artistic patterns. In an age without technology, he mastered these designs through the tedious and time consuming handiwork. Later, several attempts were made by the researchers to generate these patterns through sub-patterns, called motifs, repetitively through a computer algorithm. Currently there are two programs -- a C++ program and a Java application that recursively replicate and create these hyperbolic tessellations. The focus of this paper is to enhance and extend the existing Java application by providing interactive capabilities and adding more complex hyperbolic curves namely hyperbolic circles and horocycles. It enables user to load an existing data file or create a new data file that defines the sub-pattern and other required information pertaining to the design. The program will take that information and generate the repeating hyperbolic pattern for the user. The user can also modify the pattern by using the rich user interface and save it as a data file.