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