The Colours of Infinity

1. Front Matter

   Pages i-x

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2. The Nature of Fractal Geometry

   • Ian Stewart

   Pages 2-23

3. Exploring the Fractal Universe

   • Arthur C. Clarke

   Pages 24-37

4. A Geometry Able to Include Mountains and Clouds

   • Benoît Mandelbrot

   Pages 38-57

5. Fractal Transformations

   • Michael Barnsley, Louisa Barnsley

   Pages 58-73

6. Fractal Limits: The Mandelbrot Set and the self-similar tilings of M. C. Escher

   • Will Rood

   Pages 74-87

7. Self-organization, Self-regulation, and Self-similarity on the Fractal Web

   • Gary William Flake, David M. Pennock

   Pages 88-118

8. Fractal Financial Fluctuations

   • Benoît Mandelbrot

   Pages 120-134

9. Filming The Colours of Infinity

   • Nigel Lesmoir-Gordon

   Pages 136-143

10. The Colours of Infinity-The Film Script

    • Arthur C. Clarke

    Pages 144-172

11. Back Matter

    Pages 173-207

    PDF

A geometry able to include mountains and clouds now exists. I put it together in 1975, but of course it incorporates numerous pieces that have been around for a very long time. Like everything in science, this new geometry has very, very deep and long roots. Benoît B. Mandelbrot Introduction This enhanced and expanded edition of THE COLOURS OF INFINITY features an additional chapter on the money markets by the fractal master himself, Professor Benoît Mandelbrot. The DVD of the film associated with this book has been re-mastered especially for this edition with exquisite new fractal animations, which will take your breath away! Driven by the curious enthusiasm that engulfs many fractalistas, in 1994, Nigel Lesmoir-Gordon overcame enormous obstacles to raise the finance for, then shoot and edit the groundbreaking TV documentary from which this book takes its name. The film has been transmitted on TV channels in over fifty countries around the world. This book is not just a celebration of the discovery of the Mandelbrot set, it also brings fractal geometry up to date with a gathering of the thoughts and enthusiasms of the foremost writers and researchers in the field. As Ian Stewart makes clear in the opening chapter, there were antecedents for fractal geometry before 1975 when Mandelbrot gave the subject its name and began to develop the underlying theory.

• Fractal
• Fractals
• Natur
• Self-similarity
• organization
• complexity

From the reviews of the second edition:

“The book contains nine chapters in all, with contributions from well-known figures such as Arthur C. Clarke, Benoit Mandelbrot, Ian Stewart and Michael Barnsley. … One good feature … is that rather than simply considering fractals from a theoretical point of view, an effort has been made to discuss practical applications of this interesting area of mathematics. For those who are new to the notion of fractals, this book might be worth considering … .” (Martin Griffiths, The Mathematical Gazette, Vol. 97 (539), July, 2013)

“A more up-to-date survey of the developments in the field of fractal geometry since the documentary was released. … this book provides an attractive advert for the mathematical study of fractals. Together with the corresponding documentary, it should inspire those encountering the subject for the first time to want to explore it more.” (David A. Croydon, Mathematical Reviews, January, 2013)

“This enhanced and expanded edition of the book features chapters written both by the leading experts in the field of fractal geometry and by the contributors to the film. … The book contains dozens of breath taking photographs, and the documentary … has been digitally re-mastered to include amazing new fractal animations. Both the book and the film provide plenty of useful facts about fractals in a very inspiring, delightful and aesthetically pleasant form. Warmly recommended!” (Svitlana P. Rogovchenko, Zentralblatt MATH, Vol. 1215, 2011)

• Gordon Films UK, Bedfordshire, United Kingdom

  Nigel Lesmoir-Gordon

Nigel Lesmoir-Gordon: Producer and Director of the original documentary, he has been an independent film and documentary maker since the 1960s. He is the co-author of Introducing Fractals with Will Rood and Ralph Edney and is currently investigating the educational applications of fractal geometry.

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