### Why I am writing this

This book stems from my discovering something I really wanted to to, something I could only do properly once I knew enough mathematics. Time and again the mathematics involved was stuff that somebody had tried to teach me once, but which at the time had seemed both pointless and difficult, and hence not worth bothering with. I should think almost everyone has had an encounter like that with mathematics at some point. For me it came a lot later in life than for most people - I got as far as studying mathematics at university, and even managed to come away with a degree. But, by the end of my time at university I was pretty well finished with mathematics, and it was to be over fifteen years before my interest in it was rekindled.

The something that I discovered, and that much of this book is about, was the use of computer programs to generate images (and, to a lesser extent, music), which, at least in my eyes (ears), could attain a stunning level of beauty. I wanted to be able to create such images for myself. As I learned more about them I began to appreciate the fundamental importance of symmetry in such images, and later on how symmetry was a key concept both in mathematics, and also in sciences such as physics.

I hope both that you will enjoy the images, and that you will learn to recognise and understand works by real artists and crastsmen that use or depend on similar symmetries. If you are a teacher of mathematics I hope I might give you some ideas on how to make mathematics more interesting to some of your students. If you are an artist I hope some of the techniques and patterns in the book will inspire your own work.

So now you know why I am writing, and what I am hoping to achieve by it, it is time to find out how I intend to go about it, and so here is a Road Map.