SuperFractals

Michael Fielding Barnsley (Australian National University, Canberra)

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Hardback

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English

Cambridge University Press
07 September 2006

Mathematics & Sciences; Calculus & mathematical analysis; Fractal geometry; Mathematical modelling; Image processing

SuperFractals, first published in 2006, is the successor to Fractals Everywhere, in which the power and beauty of Iterated Function Systems were introduced and applied to producing startling and original images that reflect complex structures found for example in nature. This provoked the question of whether there is a deeper connection between topology, geometry, IFS and codes on the one hand and biology, DNA and protein development on the other. Now, 20 years later, Barnsley explains how IFS have developed in order to address this issue. Ideas such as fractal tops and superIFS are introduced, and the classical deterministic approach is combined with probabilistic ideas to produce new mathematics and algorithms that open a whole theory that could have applications in computer graphics, bioinformatics, economics, signal processing and beyond. For the first time these ideas are explained in book form, and illustrated with breathtaking pictures.

By: Michael Fielding Barnsley (Australian National University Canberra)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 248mm, Width: 181mm, Spine: 27mm
Weight: 1.080kg
ISBN: 9780521844932
ISBN 10: 0521844932
Pages: 464
Publication Date: 07 September 2006
Audience: General/trade , Professional and scholarly , ELT Advanced , Undergraduate
Format: Hardback
Publisher's Status: Active

Michael Barnsley is a Professor at the Mathematical Sciences Institute, Australian National University.

Reviews for SuperFractals

'Overall, SuperFractals would be a superb addition to the bookshelves of any scientists who use fractal analysis techniques in their research, be they physicist, biologist or economist. The author concludes by promising that the introduction of superfractals will revolutionize the way mathematics, physics, biology and art are combined, to produce a unified description of the complex world in which we live. After reading this book I have no doubt he is correct.' J. R. Mureika, Nature 'Each new idea is preceded by an intuitive discussion, often accompanied by examples, and always by gorgeous artwork. The explanation and arguments are very clear and easy to follow, even for someone not accustomed to mathematical texts.' Journal of Statistical Physics '...I can recommend the book as a nice introduction to the subject of superfractals as well as to the theory of IFS's in general. It is particularly suitable for non-geometrists as well as for non-mathematicians. From my own experience, it serves well as a textbook, also for undergraduate students.' Zentralblatt MATH 'Michael Barnsley is a wonderful guide into the world of Super Fractal geometry. This book will take you on a journey of discovery that will make you look at everyday geometry in a very different way. ...a must read for anyone who is interested in the way mathematics can be used to develop understanding in nature.' Mathematics TODAY