Complex Dynamics and Computer Experimentation

点击翻译按钮获取中文摘要

The availability of the computer as a tool for research has enabled mathematicians to make great progress in understanding chaotic behavior in nature. The resulting body of knowledge is fascinating not only because it models physical phenomena but also because it leads to colorful, visually appealing, geometric forms. Moreover, the knowledge of mathematics required to explore these ideas is minimal. Anyone with an understanding of elementary algebra and access to a modest microcomputer can create computer images of chaotic sets and can study their structure. This project will create a textbook that will make these ideas and activities available for secondary school students. The book will introduce students to the ideas of complex dynamics, fractals, and chaos. It will include simple computer programs that will enable students to generate their own fractal images. Several very high resolution computer generated images will be featured in the book, many in color. Each chapter will contain a series of projects or exercises designed to involve students in the exploration of the relevant mathematics. The book will be field tested at sites in Massachusetts, Virginia, and Minnesota. It will be published by a commercial publisher. The project director, Robert Devaney, is a well known researcher in the field of complex dynamics.