The term "spiral" is used generically to describe any geometrical smooth curve, or collection of discrete points, that winds about a central point or axis while also receding from it. One goal of this book is to emphasize the important and conspicuous role that spirals play in science and, in some cases, to show the reader how to create such spirals using a computer. Another goal is to demonstrate how research in simple mathematical formulas can reveal an inexhaustible new reservoir of magnificent shapes and images. Indeed, structures produced by these equations include shapes of startling intricacy. The graphics experiments presented, with the variety of accompanying parameters, are good ways of characterizing the complexity of such behavior.