Abrazolica

Pattern Generation for Computational Art, by Stefan Hollos and J. Richard Hollos

We've got a new book out: Pattern Generation for Computational Art.

This book shows how to turn computer generated number sequences into intricate visual patterns. The sequences are strings of the binary numbers 0 and 1 which are translated into drawing instructions to produce beautiful patterns. These patterns provide a glimpse of the hidden platonic world of mathematics.

There are 327 images in this 375 page book. Some of them can be seen here. We've also made some videos. Since the method of creating the images from binary data is so general, the same procedure can also be used to visually explore experimental data.

The book starts with Christoffel words and Sturmian sequences which are derived from the continued fraction expansion of rational and irrational numbers. It then moves on to Automatic sequences such as the Thue-Morse and Rudin-Shapiro sequences which are various ways of calculating digital roots of the integers. The first part of the book ends with sequences generated by folding paper.

Translating a sequence into drawing instructions is done using a finite automaton. This is a very general method for translating sequences that allows the same sequence to produce many different patterns. No prior experience with finite automata is necessary. All the background needed is explained in the book.

The second part of the book is devoted to L-systems which is another way of producing a string of drawing instructions. Here the strings are produced by an iterative symbol substitution process. The images produced often have a self similar fractal structure. It is possible to create many images that resemble plants. The book shows how to use an automaton and context free grammars to systematically look at all L-systems of a particular type.

All software used to create the sequences and images in the book are free for readers to download from the book's webpage. The software consists of small programs written in the C programming language that can be run on all major operating systems. There are an infinite variety of images you can generate using the software that comes with this book, providing a computational image generation lab.

This book is available now at Amazon as a paperback, or as a Kindle ebook, and it can also be gotten from us as a pdf ebook.