The Science of Fractal Images

by Heinz-Otto Peitgen (Contributor), Dietmar Saupe (Editor), Yuval Fisher (Contributor)

This book is based on notes for the course 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.

Genres: Science, Stem, Mathematics, Art, Reference, Nonfiction

326 pages, Paperback

First published July 19, 1988

About the author

Peitgen studied mathematics, physics and economics from 1965 until 1971 in Bonn, later working for six years at the Institute for Applied Mathematics at the University of Bonn under Christian Fenske, where he received his PhD in 1973. His doctoral dissertation was Asymptotische Fixpunktsätze und Stabilität (en: Asymptotic fixed-point theorems and stability).

After receiving his habilitation in 1977, he first taught as private docent in Bonn before obtaining a professorship for mathematics at the University of Bremen.

In 1986 Peitgen and Peter Richter published their lavishly illustrated and very influential book The Beauty of Fractals, which was amongst the first books popularizing the concept of fractals to the general public. This book was followed up in 1988 by The Science of Fractal Images and in 1992 by a large and authoritative volume entitled Chaos and Fractals: New Frontiers of Science, written in collaboration with Hartmut Jürgens and Dietmar Saupe.

Peitgen is director of the Centre for Complex Systems and Visualization (Centrum für Complexe Systeme und Visualisierung - CeVis) at the University of Bremen. His research work emphasises dynamical systems, numerical analysis, image analysis, and data analysis, as well as the use of computers in image-based medical diagnostics.

Reviews

[Robu-sensei · Rating 4 out of 5]

An excellent, if non-transparent, introduction to fractals, with emphasis on computer graphics. Includes detailed algorithms in "pseudo-code" (approximately Pascal) for drawing Julia sets and the Mandelbrot set, as well as simpler fractal shapes such as the Koch snowflake. The book is studded with high-resolution images that are impressive even in the present day, and astonishing for 1988 (the date of publication). A note of warning: most of the material is written for students with a strong background in mathematics.

[Cyanide Bunny · Rating 2 out of 5]

very superficial with lots of pretty pictures. the only reason i gave it an extra star is because it's just the right size for my laptop, so i can rest my computer on my legs without getting hot. Not too heavy, but this book has served me well for 6 years now with no sign of letting up.

[Robert Pulse]

10% complete - Excellent book - just what I wanted - but the math is challenging - I am having to look up symbols and get definitions – will reread many times – wish it came with a CDROM of examples and programs to play with.