author : Heinz-Otto Peitgen

Contents

• Benoit B. Mandelbrot. Forward: People and events behind the Science of Fractal Images. 1988

• Richard F. Voss. Fractals in Nature: from characterization to simulation. 1988

• Dietmar Saupe. Algorithms for Random fractals. 1988

• Robert L. Devaney. Fractal patterns arising from chaotic dynamical systems. 1988

• Heinz-Otto Peitgen. Fantastic deterministic fractals. 1988

• Michael F. Barnsley. Fractal modelling of real world images. 1988

• Benoit B. Mandelbrot. Fractal landscapes without creases and with rivers. 1988

• Michael McGuire. An eye for fractals. 1988

• Dietmar Saupe. A unified approach to fracal curves and plants. 1988

• Yuval Fisher. Exploring the Mandelbrot set. 1988

This wonderful pair of books form the perfect intermediate between the mathematics-free glossy coffee table and popular books about chaos, and the learnèd, post-graduate level tomes and research papers. Together, these well-written, well-illustrated books are packed with information and examples, and cover most of the fundamentals of fractals and chaos theory, even managing to cram in chapters slightly off the beaten track, such as the one on 'growing' fractals using L-systems.

Not light reading, but very rewarding after a bit of concentration. The mathematical sophistication required probably never goes beyond that of a physical science undergraduate course, and some is probably school level.

Highly recommended.

Part One, introduction to fractals and chaos.

1. The Backbone of Fractals: feedback and the iterator
2. Classical Fractals and Self-similarity
3. Limits and Self-similarity
4. Length, Area and Dimension: measuring complexity and scaling properties
5. Encoding Images by Simple Transformations
6. The Chaos Game: how randomness creates deterministic shapes
7. Irregular Shapes: randomness in fractal constructions

The second of this highly recommended wonderful pair of books.

Part Two, complex systems and Mandelbrot set.

8. Recursive Structures: growing fractals and plants
9. Pascal's Triangle: cellular automata and attractors
10. Deterministic Chaos: Sensitivity, mixing, and periodic points
11. Order and Chaos: period-doubling and its chaotic mirror
12. Strange Attractors: the locus of chaos
13. Julia Sets: fractal basin boundaries
14. The Mandelbrot Set: ordering the Julia sets