Short works

Books : reviews

Heinz-Otto Peitgen, Peter H. Richter.
The Beauty of Fractals: images of complex dynamical systems.
Springer. 1986

Heinz-Otto Peitgen, Dietmar Saupe, eds.
The Science of Fractal Images.
Springer. 1988


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

Heinz-Otto Peitgen, Hartmut Jurgens, Dietmar Saupe.
Fractals for the Classroom Part 1: Introduction to Fractals and Chaos.
Springer. 1992

rating : 1.5 : unmissable
review : 31 May 1997

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

Heinz-Otto Peitgen, Hartmut Jurgens, Dietmar Saupe.
Fractals for the Classroom Part 2: Complex Systems and Mandelbrot Set.
Springer. 1992

rating : 1.5 : unmissable
review : 31 May 1997

The second of this highly recommended wonderful pair of books.

Part Two, complex systems and Mandelbrot set.

  1. Recursive Structures: growing fractals and plants
  2. Pascal's Triangle: cellular automata and attractors
  3. Deterministic Chaos: Sensitivity, mixing, and periodic points
  4. Order and Chaos: period-doubling and its chaotic mirror
  5. Strange Attractors: the locus of chaos
  6. Julia Sets: fractal basin boundaries
  7. The Mandelbrot Set: ordering the Julia sets