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The Colours Of Infinity

Author: Nigel Lesmoir-Gordon
Publisher: Springer Science & Business Media
ISBN: 9781849964869
Size: 59.81 MB
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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.

Introducing Fractals

Author: Nigel Lesmoir-Gordon
Publisher: Icon Books Ltd
ISBN: 1848317832
Size: 24.22 MB
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From Zeno to Mandelbrot: explore this new language with which you can describe the shape of cloud as precisely as an architect can describe a house.

Chaos And Fractals

Author: Heinz-Otto Peitgen
Publisher: Springer Science & Business Media
ISBN: 1475747403
Size: 24.44 MB
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For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.

The Beauty Of Fractals

Author: Heinz-Otto Peitgen
Publisher: Springer Science & Business Media
ISBN: 3642617174
Size: 23.49 MB
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Now approaching its tenth year, this hugely successful book presents an unusual attempt to publicise the field of Complex Dynamics. The text was originally conceived as a supplemented catalogue to the exhibition "Frontiers of Chaos", seen in Europe and the United States, and describes the context and meaning of these fascinating images. A total of 184 illustrations - including 88 full-colour pictures of Julia sets - are suggestive of a coffee-table book. However, the invited contributions which round off the book lend the text the required formality. Benoit Mandelbrot gives a very personal account, in his idiosyncratic self-centred style, of his discovery of the fractals named after him and Adrien Douady explains the solved and unsolved problems relating to this amusingly complex set.

The Butterfly In The Quantum World

Author: Indubala I Satija
Publisher: Morgan & Claypool Publishers
ISBN: 1681741172
Size: 47.72 MB
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Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today. The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul.

Fractal 3d Magic

Author:
Publisher: Sterling Publishing Company Incorporated
ISBN: 9781454912637
Size: 14.31 MB
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Filled with more than 200 intricate and eye-popping 3D designs, which can be viewed with the accompanying 3D glasses, a rare glimpse into the world of computer-generated fractal art provides background on everything from the classic Mandelbrot set to ethereal fractal flames. Original.

Chaos And Fractals

Author: C.A. Pickover
Publisher: Elsevier
ISBN: 9780080528861
Size: 58.22 MB
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These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art. Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art. Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

The Dark Arrow Of Time

Author: Massimo Villata
Publisher: Springer
ISBN: 3319674862
Size: 73.70 MB
Format: PDF, Kindle
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This riveting scientific novel combines adventure, love, suspense, magic, pathos, and mystery in a carefully woven plot that is full of unexpected twists and turns. The author is an astrophysicist who has developed an alternative theory, which holds that traveling in time is possible. Time is, in fact, the real protagonist of the novel and of the intrigue surrounding the attempt to seize the secret of Time’s other arrow, the dark arrow normally hidden from us, which points back at our past. The underlying premise is that antimatter is nothing more than common matter moving backwards in time. The justification for this interpretation has been with us for some time, “hiding in plain sight” within Maxwell’s equations, the Lorentz transformations, the CPT theorem of relativistic quantum mechanics, and Feynman diagrams. While the science underlying the narrative is explained whenever necessary, sometimes with the aid of simple mathematical formulas, these scientific asides account for only a small part of the book, which will appeal to a wide audience, including readers who are far from being science buffs.

Weird Universe

Author: David A. J. Seargent
Publisher: Springer
ISBN: 3319107380
Size: 78.65 MB
Format: PDF, Kindle
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As new discoveries complicate the scientific picture of the universe, the evolving theories about the nature of space and time and the origins and fate of the universe threaten to become overwhelming. Enter David Seargent. Continuing the author's series of books popularizing strange astronomy facts and knowledge, Weird Universe explains the bizarre, complicated terrain of modern cosmology for lay readers. From exploring some of the strange consequences of the theories of special and general relativity, to probing time dilation and the twin and mother-and-baby “paradoxes” and the theory that the universe can be mathematically considered as a hologram, all of the latest findings and conjectures are clearly described in non-technical language. The development of quantum physics and the more recent developments of string and M-theory are looked at, in addition to several hypotheses that have not won wide acceptance from the scientific community, such as modified gravity. Enter the wonderfully weird world of these theories and gain a new appreciation for the latest findings in cosmological research.