Preface

Summary

Fractals came onto the stage in the 1970's with the emergence of the Mandelbrot set, with its incredibly complicated and interesting boundary. During the 1980's a number of books appeared, including most especially by Mandelbrot, Barnsley and Devaney, that gave a mathematical background for fractals that made fractals accessible to both students and teachers. More recently, as computers and their users have become more sophisticated, the domain of fractals has broadened, from art to scientific application to mathematical analysis. In particular, students in high school as well as college are often introduced to fractals and fractal concepts. The present volume includes six essays related to fractals, with perspectives different enough to give you a taste of the breadth of the subject.

Each essay is self-contained and expository. Moreover, each of the essays is intended to be accessible to a broad audience that includes college teachers, high school teachers, advanced undergraduate students, and others who wish to learn or teach about topics in fractals that are not regularly in textbooks on fractals.

Next is a brief overview of each essay; together these overviews should give you quite different views of the topic of fractals.

volume begins with “Mathscapes—Fractal Geometry,” by Anne M. Burns. Burns, who is an artist as well as a mathematician, discusses several ways of modeling on the computer such fractal objects as plant growth and trees, clouds and mountains. The algorithms that Burns uses to create such fascinating and beautiful fractal scenery include stochastic matrices, simple recursion, and a probabilistic method, all of which are accessible to students in a variety of courses from mathematics to programming to graphics.