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Chaos and Fractals
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Chaos and Fractals: An Elementary Introduction

David P. Feldman

Abstract

This book provides an elementary introduction to chaos and fractals. It introduces the key phenomena of chaos — aperiodicity, sensitive dependence on initial conditions, bifurcations — via simple iterated functions. Fractals are introduced as self-similar geometric objects and analysed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia sets and the Mandelbrot set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.

Keywords: chaos, fractals, calculus, physics, aperiodicity, bifurcations, geometric objects, self-similarity, Julia sets, Mandelbrot set

Bibliographic Information

Print publication date: 2012 Print ISBN-13: 9780199566433
Published to Oxford Scholarship Online: December 2013 DOI:10.1093/acprof:oso/9780199566433.001.0001

Authors

Affiliations are at time of print publication.

David P. Feldman, author
Department od Physics and Mathematics, College of the Atlantic, Bar Harbor, Maine, USA

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