Programming for Patterns & Mathematical Art

This book is a practical introduction for anyone who would like to write computer programs to create digital art from mathematics. It covers patterns, and other mathematical art, arising from cellular automata, fractals, Islamic design, chaotic symmetry, the 1840’s Harmonograph and the rolling discs of the Spirograph. Along the way, we will simulate epidemics and forest fires and create forests of fractal trees. Ants will scurry about their anthills and our virtual Harmonograph will visualise the fascinating patterns produced by musical notes as they decay over time. The Spirograph will create patterns which are impossible to make with the real thing, tirelessly, and without mistakes and broken pencils. You will watch beautiful symmetry emerge from mathematical chaos and discover the strangest creatures and exotic structures lurking within fractals. You will create images of centuries-old Islamic designs in which you can change colours, lines and scale. Above all, you will be stimulated to improve the programs, add new data, find new colouring schemes, explore the huge breadth of possibilities in each topic and, of course, take your computing skills in any other direction you wish. The necessary maths and the computing language (Visual Basic) are reviewed and explained, and the full, annotated codes for all 24 programs are given. The book has over 300 illustrations, including 160 stunning images created by the programs. Substantial additional data is provided to create many more, and the program interfaces are flexible, allowing experimental data and colour schemes to be tried at will.