Fractals and Chaos An illustrated course [Paperback]

Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study.INTRODUCTION
Introduction
A matter of fractals
Deterministic chaos
Chapter summary and further reading

REGULAR FRACTALS AND SELF-SIMILARITY
Introduction
The Cantor set
Non-fractal dimensions: the Euclidean and topological dimension
The similarity dimension
The Koch curve
The quadratic Koch curve
The Koch island
Curves in the plane with similarity dimension exceeding 2
The Sierpinski gasket and carpet
The Menger Sponge
Chapter summary and further reading
Revision questions and further tasks

RANDOM FRACTALS
Introduction
Randomizing the Cantor set and Koch curve
Fractal boundaries
The box counting dimension and the Hausdorff dimension
The structured walk technique and the divider dimension
The perimeter-area relationship
Chapter summary and further reading
Revision questions and further tasks

REGULAR AND FRACTIONAL BROWNIAN MOTION
Introduction
Regular Brownian motion
Fractional Brownian motion: time traces
Fractional Brownian surfaces
Fractional Brownian motion: spatial trajectories
Diffusion limited aggregation
The colorl“*