Symmetry in Chaos

A Search for Pattern in Mathematics, Art and Nature, Second Edition


Author: Michael Field,Martin Golubitsky

Publisher: SIAM

ISBN: 0898716721

Category: Mathematics

Page: 199

View: 6089

A striking full-colour book which explores how combining symmetry and chaos can lead to the construction of remarkable images. This book is an engaging look at the interplay of art and mathematics, and between symmetry and chaos. The underlying mathematics involved in the generation of the images is described.

Symmetry in Chaos

A Search for Pattern in Mathematics, Art, and Nature, Second Edition


Author: Michael Field,Martin Golubitsky

Publisher: SIAM

ISBN: 9780898717709

Category: Chaotic behavior in systems

Page: 199

View: 2073

Symmetry suggests order and regularity whilst chaos suggests disorder and randomness. 'Symmetry in Chaos' is an exploration of how combining seemingly contradictory principles can lead to the construction of striking and beautiful images. This book is an engaging look at the interplay of art and mathematics.

Symmetry in Chaos

A Search for Pattern in Mathematics, Art and Nature


Author: Mike Field,Michael Field

Publisher: Oxford University Press, USA


Category: Literary Criticism

Page: 218

View: 5985

In fifty-four colour plates, Symmetry in Chaos illustrates the many varied and beautiful pictures that may be produced when the seemingly contradictory ideas of symmetry and chaos are combined. The mathematical ideas behind these pictures are presented in an elementary fashion, and computer programs are provided in appendices. These programs allow the reader to generate on a home computer black and white versions of the many and varied patterns shown throughout this book. The authorshad two reasons for writing this book: to present the surprisingly beautiful and intricate pictures that are produced by combining symmetry and chaos, and to present in as elementary a way as possible the mathematical ideas that lead to these pictures.

Mathematics in Nature

Modeling Patterns in the Natural World


Author: John A. Adam

Publisher: Princeton University Press

ISBN: 1400841011

Category: Mathematics

Page: 392

View: 8520

From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.

Computers, Pattern, Chaos and Beauty


Author: Clifford A. Pickover

Publisher: Courier Corporation

ISBN: 0486151611

Category: Science

Page: 416

View: 4408

Fractals and chaos theory lead to startling graphics in this book by a renowned scientist, inventor, and artist, who coordinates information from disparate fields. Over 275 illustrations, 29 in color.

The Pattern Book: Fractals, Art, and Nature


Author: Clifford A Pickover

Publisher: World Scientific

ISBN: 9814504033

Category: Mathematics

Page: 464

View: 5163

This book will allow you to travel through time and space. To facilitate your journey, the editor has scoured the four corners of the earth in a quest for unusual people and their fascinating patterns. From Mozambique, to Asia, to many European countries, the contributors to The Pattern Book include world-famous cancer researchers, little-known artists and eclectirc computer programmers. Some of the patterns are ultramodern, while others are centuries old. Many of the patterns are drawn from the universe of mathematics. Computer recipes are scattered throughout. Although the emphasis is on computer-generated patterns, the book is informal and the intended audience spans several fields. The emphasis is on the fun that the true pattern lover finds in doing, rather than in reading about the doing! The book is organized into three main parts: Representing Nature (for those patterns which describe or show real physical phenomena, e.g., visualizations of protein motion, sea lilies, etc.), Mathematics and Symmetry (for those patterns which describe or show mathematical behavior, e.g. fractals), and Human Art (for those patterns which are artistic works of humans and made without the aid of a computer, e.g. Moslem tiling patterns.) Contents:Representing NatureMathematics and SymmetryHuman Art Readership: Computer graphic scientists, computer scientists, artists and mathematicians. keywords:Fractals;Pattern;Computer Graphics;Computer Art;Scientific Visualization;Mathematics;Mandelbrot Set;Tilings;Symmetry;Beauty;Aesthetics;Nature “Fractals can be found everywhere, and Clifford Pickover has done a good job in selecting some of the best. The range of the collection is considerable, from ‘Wood Pattern’ to ‘Trajectories of A Neural Network Quantizer in Rhythm Space’. And all posses a simplistic beauty that justifies the presence of art in the title. Such creations, possessing enormous complexity from very simple origins, truly force us to stretch our imaginations. All of the generation processes are very easy to understand, and some modifications for additional exploration are obvious … One more in the collection of works devoted to fractals, this book ranks among the easiest to understand. A natural first book for those interested in fractals as objects of mathematical study or art.” Charles Ashbacher Journal of Recreational Mathematics “Artists, scientists, and computer enthusiasts will be delighted by this inspiring collection of visually striking patterns with accompanying explanations and references.” Julien C Sprott Strange Attractors: Creating Patterns in Chaos “The Pattern Book: Fractals, Art, & Nature — fascinating! A feast for both the eyes and mind! … This book helps us gain insights on how patterns are created and their scientific connections, while letting us enjoy the impact of their visual beauty. A must for those interested in science, nature, or art.” div style="text-align: right;">Theoni Pappas The Joy of Mathematics and The Magic of Mathematics “Particularly noteworthy are the many contributions by Dr. I D Entwistle, whose name is well known to readers of Fractal Report. The images submitted by him show outstanding originality and artistry; of their class they are unique. Other contributors worthy of special mention here include Earl F Glynn and Mieczyszlaw Szyszkowicz for their striking and original images … This beautifully illustrated and informative book can be highly recommended.” C J Freeman Fractal Report “Interesting introduction to the world of patterns.” The American Mathematical Monthly “The patterns, many in black and white, some in color, are generally intricate and beautiful. Pseudocode and code are provided for many of the patterns. The book stimulates experiment. An excellent resource for entry into the world of patterns. Recommended for artists, scientists, and computer enthusiasts, undergraduates through professionals.” G J G Junevicus Choice “The Pattern Book is a visual smorgasbord … My first prize goes to the microphotograph of leaf structure showing its dendritic and fractal character.” The Chemical Intelligencer

Crystal and Dragon

The Cosmic Dance of Symmetry and Chaos in Nature, Art and Consciousness


Author: David Wade

Publisher: Inner Traditions / Bear & Co

ISBN: 9780892814046

Category: Art

Page: 287

View: 778

Exploring the interplay of light and darkness, order and chaos, David Wade shows how perceptions about the nature of the universe are reflected in the art of a given period. He details the form and fluidity of prehistoric art, the crystalline order of Islamic patterns, and the subtle vitality of Chinese landscapes and calligraphy.

What Shape is a Snowflake?


Author: Ian Stewart

Publisher: N.A

ISBN: 9780297607236

Category: Mathematics in nature

Page: 224

View: 1926

An enlightening vision of how the laws of mathematics find organic expression in the beauty and patterns of nature, written by an acclaimed mathematician and science writer.

Symmetry: A Very Short Introduction


Author: Ian Stewart

Publisher: OUP Oxford

ISBN: 0199651981

Category: Mathematics

Page: 160

View: 361

Symmetry is an immensely important concept in mathematics and throughout the sciences. In this Very Short Introduction, Ian Stewart highlights the deep implications of symmetry and its important scientific applications across the entire subject.

Frontiers of Complexity

The Search for Order in a Chaotic World


Author: Peter V. Coveney

Publisher: Ballantine Books

ISBN: 9780449910818

Category: Science

Page: 462

View: 4260

A groundbreaking book explores the dynamic, emerging concept of complexity and its relationship to mathematics, physics, biology, and chemistry, and provides an arresting account of how far science has come and what to expect in the rapidly approaching future. Reprint.

Nature's Numbers

The Unreal Reality Of Mathematics


Author: Ian Stewart

Publisher: Basic Books

ISBN: 0786723920

Category: Science

Page: 176

View: 6027

States that the mental construct of mathematics can provide humankind with a key tool to understanding the world, and discusses the implications of basic math concepts

Patterns in Nature

Why the Natural World Looks the Way It Does


Author: Philip Ball

Publisher: University of Chicago Press

ISBN: 022633256X

Category: Nature

Page: 288

View: 8267

Though at first glance the natural world may appear overwhelming in its diversity and complexity, there are regularities running through it, from the hexagons of a honeycomb to the spirals of a seashell and the branching veins of a leaf. Revealing the order at the foundation of the seemingly chaotic natural world, Patterns in Nature explores not only the math and science but also the beauty and artistry behind nature’s awe-inspiring designs. Unlike the patterns we create in technology, architecture, and art, natural patterns are formed spontaneously from the forces that act in the physical world. Very often the same types of pattern and form – spirals, stripes, branches, and fractals, say—recur in places that seem to have nothing in common, as when the markings of a zebra mimic the ripples in windblown sand. That’s because, as Patterns in Nature shows, at the most basic level these patterns can often be described using the same mathematical and physical principles: there is a surprising underlying unity in the kaleidoscope of the natural world. Richly illustrated with 250 color photographs and anchored by accessible and insightful chapters by esteemed science writer Philip Ball, Patterns in Nature reveals the organization at work in vast and ancient forests, powerful rivers, massing clouds, and coastlines carved out by the sea. By exploring similarities such as those between a snail shell and the swirling stars of a galaxy, or the branches of a tree and those of a river network, this spectacular visual tour conveys the wonder, beauty, and richness of natural pattern formation.

Spiral Symmetry


Author: I Hargittai,C A Pickover

Publisher: World Scientific

ISBN: 9814506265

Category: Science

Page: 468

View: 7319

From the tiny twisted biological molecules to the gargantuan curling arms of many galaxies, the physical world contains a startling repetition of spiral patterns. Today, researchers have a keen interest in identifying, measuring, and defining these patterns in scientific terms. Spirals play an important role in the growth processes of many biological forms and organisms. Also, through time, humans have imitated spiral motifs in their art forms, and invented new and unusual spirals which have no counterparts in the natural world. Therefore, one goal of this multiauthored book is to stress the conspicuous role that spirals play in science, and to show the reader how to create such spirals using a computer. Another goal is to show how simple mathematical formulas can reveal magnificent shapes and images. This interdisciplinary book revolves around a common theme, spiral symmetry, and is intended for scientists, humanists, and interested laypeople. Contents: The Spiral in Nature, Myth, and Mathematics (J Kappraff)Does the Golden Spiral Exists, and if not, where is its Center (A L Loeb & W Varney)Pythagorean Spirals (E J Eckert)Dynamical Spirals (A V Holden)Random Spirals (W A Seitz & D J Klein)Spiral Galaxies (B G Elmegreen)Spiral-Based Self-Similar Sets (K Wicks)Symmetry and Spirals: An Artist's Personal Statement (R Newman)Spiral Structures in Julia Sets and Related Sets (M Michelitsch & O E Rössler)Electromagnetic Theory of Chiral Media (A Lakhtakia)Isometric Systems in Isotropic Space: An Artist's Personal Statement on Spiral and other Map Projections (A Denes)On the Origins of Spiral Symmetry in Plants (R V Jean)and other papers Readership: Scientists, humanists and interested laypeople. keywords:Spirals;Symmetry;Fractals;Computer Graphics;Computer Art;Botany;Mathematics;Phyllotaxis;Beauty;Aesthetics;Nature

Chaos and Fractals

A Computer Graphical Journey


Author: C.A. Pickover

Publisher: Elsevier

ISBN: 9780080528861

Category: Computers

Page: 452

View: 1346

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 Beauty of Numbers in Nature

Mathematical Patterns and Principles from the Natural World


Author: Ian Stewart

Publisher: N.A

ISBN: 9781782404712


Page: 224

View: 2944

Think of a zebra's stripes, the complexities of a spider's web, the uniformity of desert dunes, or the spirals in a sunflower head ... think of a snowflake. The Beauty of Numbers in Nature shows how life on Earth forms the principles of mathematics. Starting with the simplest patterns, each chapter looks at a different kind of patterning system and the mathematics that underlies it. In doing so the book also uncovers some universal patterns, both in nature and man-made, from the basic geometry of ancient Greece to the visually startling fractals that we are familiar with today. Elegantly illustrated, The Beauty of Numbers in Nature is an illuminating and engaging vision of how the apparently cold laws of mathematics find expression in the beauty of nature.

Symmetry, Shape, and Surfaces

An Introduction to Mathematics Through Geometry


Author: L. Christine Kinsey,Teresa E. Moore

Publisher: Springer Science & Business Media

ISBN: 9781930190092

Category: Mathematics

Page: 494

View: 956

This text is modern in its selection of topics and in the learning models used by the authors. Covers some exciting, but non-traditional topics from the subject area of geometry.

Applications of Mathematics in Models, Artificial Neural Networks and Arts

Mathematics and Society


Author: Vittorio Capecchi,Massimo Buscema,Pierluigi Contucci,Bruno D'Amore

Publisher: Springer Science & Business Media

ISBN: 9789048185818

Category: Social Science

Page: 617

View: 2657

The book shows a very original organization addressing in a non traditional way, but with a systematic approach, to who has an interest in using mathematics in the social sciences. The book is divided in four parts: (a) a historical part, written by Vittorio Capecchi which helps us understand the changes in the relationship between mathematics and sociology by analyzing the mathematical models of Paul F. Lazarsfeld, the model of simulation and artificial societies, models of artificial neural network and considering all the changes in scientific paradigms considered; (b) a part coordinated by Pier Luigi Contucci on mathematical models that consider the relationship between the mathematical models that come from physics and linguistics to arrive at the study of society and those which are born within sociology and economics; (c) a part coordinated by Massimo Buscema analyzing models of artificial neural networks; (d) a part coordinated by Bruno D’Amore which considers the relationship between mathematics and art. The title of the book "Mathematics and Society" was chosen because the mathematical applications exposed in the book allow you to address two major issues: (a) the general theme of technological innovation and quality of life (among the essays are on display mathematical applications to the problems of combating pollution and crime, applications to mathematical problems of immigration, mathematical applications to the problems of medical diagnosis, etc.) (b) the general theme of technical innovation and creativity, for example the art and mathematics section which connects to the theme of creative cities. The book is very original because it is not addressed only to those who are passionate about mathematical applications in social science but also to those who, in different societies, are: (a) involved in technological innovation to improve the quality of life; (b) involved in the wider distribution of technological innovation in different areas of creativity (as in the project "Creative Cities Network" of UNESCO).

Chaos and Fractals

New Frontiers of Science


Author: Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe

Publisher: Springer Science & Business Media

ISBN: 1475747403

Category: Mathematics

Page: 999

View: 9225

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 Symmetry Perspective

From Equilibrium to Chaos in Phase Space and Physical Space


Author: Martin Golubitsky,Ian Stewart

Publisher: Birkhäuser

ISBN: 3034881673

Category: Mathematics

Page: 325

View: 8947

The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS