Do a search for the meaning of mathematics and you are certain to find a great many definitions. Mathematics is the study of such things as quantity, structure, space, change, numbers, measurement, combination, interrelation, shape, and arrangement.

This book looks at mathematics as a search for patterns: patterns arising from arithmetic, geometry, number theory, and algebra. Some of the patterns are displayed as single pictures, but others are revealed by displaying a sequences of pictures, each picture derived from the previous one based on some rule. There is a pattern to the creation of a pattern.

​All of the examples presented in this book were developed using software you can download from this site.

​Although it can certainly stand by itself, the purpose of this book is to serve as a resource for users of my math and science software. This book discusses questions raised by that software and explains the underlying math and science concepts on which my programs are based. Like the software, the book is designed to help and encourage students of all ages to explore, see in new ways, discover patterns and solve problems. Topics include mod arithmetic, slopes, planetary motion, probability, magic squares, and recursive functions. ​​Like the software, the book is free. Note: pdf versions are much less interactive.

​This third book displays a variety of fractals that have been created using the author's own computer programs. Also included is information about how each fractal was created, in as simple terms as possible, without any programming details. Some use mod arithmetic, some use non-base 10 systems, and some use similarity transformations that paste smaller versions of the original patten onto parts of itself.