Foreword to the Project

You are looking at the outcome of a three-year project, a unique experiment in electronic publishing. For lack of a better word, we call this a package. It has three intertwined components: a book, a CD-ROM, and a website. It is perhaps the first such multimedia package devoted to an advanced branch of mathematics.

The book is the primary component, and it is extensively illustrated with monochrome computer graphics. The CD-ROM is devoted mainly to 12 computer graphic animations in color, which animate and expand the graphics in the book. The user interface to the CD-ROM is made in the style, and with the technology, of the World Wide Web. Therefore, it integrates seamlessly with the website devoted to the book and CD-ROM, which is maintained at the Visual Math Institute. This website also connects outward with the resources of the World Wide Web.

The motivation for this unique package is the conviction that this style of electronic publication is the ideal medium for mathematical communication, and especially, for the branch of mathematics known as dynamical systems theory, including our subject: noninvertible discrete chaos theory in two dimensions. The essence of this communicative style is the dynapic technique, in which a drawing is developed stroke-by-stroke, along with a carefully coordinated spoken commentary. This is the traditional method used by most mathematicians, when speaking among themselves: Visual Math!

Revised 24 September 1996 by Ralph Abraham, <>