Complex Dynamics and Computer Experimentation

计算机作为研究工具的可用性使数学家在理解自然界的混沌行为方面取得了巨大进展。由此产生的知识体系令人着迷，不仅因为它模拟了物理现象，还因为它导致了丰富多彩的、视觉上吸引人的几何形式。此外，探索这些想法所需的数学知识很少。任何懂初等代数的人，只要有一台普通的微型计算机，就能创建混沌集的计算机图像，并能研究它们的结构。这个项目将制作一本教科书，将这些想法和活动提供给中学生。本书将向学生介绍复杂动力学、分形和混沌的概念。它将包括简单的计算机程序，使学生能够生成自己的分形图像。一些非常高分辨率的计算机生成的图像将出现在书中，许多是彩色的。每章将包含一系列的项目或练习，旨在让学生参与相关数学的探索。这本书将在马萨诸塞州、弗吉尼亚州和明尼苏达州进行实地测试。它将由一家商业出版商出版。项目负责人Robert Devaney是复杂动力学领域的知名研究人员。

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.