The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot set, Julia sets, cellular automata, L-systems, percolation and strange attractors. This new edition has been thoroughly revised throughout. The appendices of the original edition were taken out since more recent publications cover this material in more depth. Instead of the focussed computer programs in BASIC, the authors provide 10 interactive JAVA-applets for this second edition.

Chaos and Fractals: New Frontiers of Science

Peitgen, Heinz-Otto

Jürgens, Hartmut

Saupe, Dietmar

Reference

Springer

This book is based on notes for the course Fractals:lntroduction, Basics and Perspectives given by MichaelF. Barnsley, RobertL. Devaney, Heinz-Otto Peit gen, Dietmar Saupe and Richard F. Voss. The course was chaired by Heinz-Otto Peitgen and was part of the SIGGRAPH '87 (Anaheim, California) course pro gram. Though the five chapters of this book have emerged from those courses we have tried to make this book a coherent and uniformly styled presentation as much as possible. It is the first book which discusses fractals solely from the point of view of computer graphics. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable. Ba sic algorithms are typically presented in pseudo-code or a description so close to code that a reader who is familiar with elementary computer graphics should find no problem to get started. Mandelbrot's fractal geometry provides both a description and a mathemat ical model for many of the seemingly complex forms and patterns in nature and the sciences. Fractals have blossomed enormously in the past few years and have helped reconnect pure mathematics research with both natural sciences and computing. Computer graphics has played an essential role both in its de velopment and rapidly growing popularity. Conversely, fractal geometry now plays an important role in the rendering, modelling and animation of natural phenomena and fantastic shapes in computer graphics.

The Science of Fractal Images

Computers & Technology

Programming

Springer, Verlag

Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating insights for the classroom teacher and integrates illustrations from a wide variety of applications with an enjoyable text to help bring the concepts alive and make them understandable to the average reader. This book will have a tremendous impact upon teachers, students, and the mathematics education of the general public. With the forthcoming companion materials, including four books on strategic classroom activities and lessons with interactive computer software, this package will be unparalleled.

Fractals for the Classroom: Part One Introduction to Fractals and Chaos

Science & Math

Mathematics

There are many reasons for writing this first volume of strategic activities on fractals. The most pervasive is the compelling desire to provide students of mathematics with a set of accessible, hands-on experiences with fractals and their underlying mathematical principles and characteristics. Another is to show how fractals connect to many different aspects of mathematics and how the study of fractals can bring these ideas together. A third is to share the beauty of their structure and shape both through what the eye sees and what the mind visualizes. Fractals have captured the attention, enthusiasm, and interest of many people around the world. To the casual observer, their color, beauty, and geometric structure captivates the visual senses like few other things they have ever experienced in mathematics. To the computer scientist, fractals offer a rich environment in which to explore, create, and build a new visual world as an artist creating a new work. To the student, fractals bring mathematics out of past history and into the twenty-first century. To the mathematics teacher, fractals offer a unique, new opportunity to illustrate both the dynamics of mathematics and its many connecting links.

Fractals for the Classroom: Strategic Activities Volume One

YUNKER, LEE

Maletsky, Evan

Perciante, Terry

Fractals for the Classroom: Part Two: Complex Systems and Mandelbrot Set

For almost 15 years chaos and fractals have been riding a wave that has enveloped many areas of mathematics and the natural sciences in its power, creativity and expanse. Traveling far beyond the traditional bounds of mathematics and science to the distant shores of popular culture, this wave captures the attention and enthusiasm of a worldwide audience. The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot Set, Julia Sets, Cellulair Automata, L- systems, Percolation and Strange Attractors. Each chapter is closed by a "Program of the Chapter" which provides computer code for a central experiment. Two appendices complement the book. The first, by Yuval Fisher, discusses the details and ideas of fractal images and compression; the second, by Carl J.G. Evertsz and Benoit Mandelbrot, introduces the foundations and implications of multifractals.

Foreign Language Study & Reference

Written by the award winning authors of Chaos and Fractals (0-387-97903-4), this work introduces the reader to iterated function systems through a lively, interactive approach. This well-written, clearly illustrated book explores the history and the unlimited potential of fractals, while developing a basic mathematical understanding and appreciation for the topics.

Fractals for the Classroom: Strategic Activities Volume Three

Computer Science

Special and Spurious Solutions of X (Memoirs of the American Mathematical Society)

Nussbaum, Roger D.

Amer Mathematical Society

Published in cooperation with the National Council of Teachers of Mathematics

See the best price to sell, buy, or rent books by Peitgen, Heinz-Otto. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Peitgen, Heinz-Otto

See the best price to sell, buy, or rent books by Peitgen, Heinz-Otto. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Chaos and Fractals: New Frontiers of Science

The Science of Fractal Images

Fractals for the Classroom: Part One Introduction to Fractals and Chaos

Fractals for the Classroom: Strategic Activities Volume One

Fractals for the Classroom: Part Two: Complex Systems and Mandelbrot Set

Chaos and Fractals: New Frontiers of Science

Fractals for the Classroom: Strategic Activities Volume Three

Special and Spurious Solutions of X (Memoirs of the American Mathematical Society)

Fractals for the Classroom: Part Two: Complex Systems and Mandelbrot Set

Chaos and Fractals: New Frontiers of Science