Synopses & Reviews
Superfractals is the long-awaited 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 brings the story up to date by explaining how IFS have developed in order to address this issue. New 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.
"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."
"The book is well structured and an enjoyable read...The book contains some interesting, very deep and even enthralling mathematics. The author's ability to clearly describe complicated phenomena paired with a pleasant writing style make this book a must read for all people interested in the mathematics of fractals...There are many wonderful, colorful pictures that spark one's imagination. Examples spread liberally throughout the book together with relevant exercises help illuminate this new look at 'patterns in nature'."
Kai Brunkalla, MAA Reviews, MathDL
"Exuberant, light-hearted, chatty, idiosyncratic, and lavishly illustrated by many beautiful and breathtaking pictures."
Lars Olsen, Mathematical Reviews
SuperFractals is about a new kind of geometry and this book explains clearly and accessibly how it is born from a union of randomness, geometry and computation. Mathematical ideas are explained and illustrated through a profusion of full-colour images. Potential applications are explored: for example, SuperFractals enable a vast improvement in terms of texture and variety than conventional computer graphics methods currently used in games and films; they may lead to insights in economics, science, medical imaging and biology; they will have application for image and signal compression.
SuperFractals describes new mathematics and algorithms for the first time in book form, with breathtaking colour pictures.
In SuperFractals, Michael Barnsley describes 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.
About the Author
Michael Barnsley is a Professor at the Mathematical Sciences Institute, Australian National University.
Table of Contents
Part I. Geometries and Transformations: 1. Codes, metrics and topologies; 2. Transformations of points, sets, pictures and measures; 3. Semigroups on sets, measures and pictures; Part II. Iterated Function Systems: 4. IFS acting on measures; 5. More on IFS; Part III. Applications to Graphics: 6. Digital content production; 7. Image compression; 8. Super IFS.