AbstractOver the last several years the authors have used computer graphics to generate, study and analyze more than 300 Islamic geometrical repeat patterns. These patterns offer a rich source for exploitation by artists and are also of interest to mathematicians, crystallographers, architects, archaeologists and others. They can serve as elegant test beds for research into hierarchical programming and texture mapping. The paper discusses the evolution of classical geometric methods for Islamic patterns and goes on to develop algorithms based on group theory for efficient generation of all crystallographic repeat patterns using modern computer graphics.