Fractal Geometry: Mathematical Foundations and Applications

by Kenneth Falconer

An accessible introduction to fractals, useful as a text or reference. Part I is concerned with the general theory of fractals and their geometry, covering dimensions and their methods of calculation, plus the local form of fractals and their projections and intersections. Part II contains examples of fractals drawn from a wide variety of areas of mathematics and physics, including self-similar and self-affine sets, graphs of functions, examples from number theory and pure mathematics, dynamical systems, Julia sets, random fractals and some physical applications. Also contains many diagrams and illustrative examples, includes computer drawings of fractals, and shows how to produce further drawings for themselves.

Genres: Mathematics, Science, Geometry

310 pages, Hardcover

First published March 30, 1990

Reviews

[Paige McLoughlin · Rating 4 out of 5]

very compressed treatment of the topic though it covers the main points and too much emphasis on mathematical rigor for my tastes but workable.

[Milan · Rating 4 out of 5]

A good undergraduate/graduate textbook for anyone interested in fractal analysis.

[Paige McLoughlin · Rating 4 out of 5]

A little more rigor than I need, but it covers most of the topics of larger volumes. This book is definitely a more mathematical treatment, but it has applications in later chapters and covers most of the sweep, including dynamical systems and power spectra regarding Brownian noise and random fractals. Also has the famous logistic equation, with period-doubling for certain values and the onset of chaos. It covers most of the stuff for mathematicians with definitions and proofs.