Author: Mike Field
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 238
Book Description
A classy rendering of chaos theory and symmetry mathematics illustrating recent understanding about the convergence between the two areas. Mathematicians Field and Golubitsky explain the relationship between chaos and symmetry, describing how chaotic process may eventually lead to symmetric patterns in a clear, understandable language and in color photographs reproducing computer images demonstrating the inherent pattern in apparent chaos. The authors compare these images with pictures from nature and art that, miraculously, mimic the computer patterns. Includes an appendix containing several BASIC programs enabling home computer owners to experiment with similar images. Annotation copyrighted by Book News, Inc., Portland, OR
Symmetry in Chaos
Author: Mike Field
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 238
Book Description
A classy rendering of chaos theory and symmetry mathematics illustrating recent understanding about the convergence between the two areas. Mathematicians Field and Golubitsky explain the relationship between chaos and symmetry, describing how chaotic process may eventually lead to symmetric patterns in a clear, understandable language and in color photographs reproducing computer images demonstrating the inherent pattern in apparent chaos. The authors compare these images with pictures from nature and art that, miraculously, mimic the computer patterns. Includes an appendix containing several BASIC programs enabling home computer owners to experiment with similar images. Annotation copyrighted by Book News, Inc., Portland, OR
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 238
Book Description
A classy rendering of chaos theory and symmetry mathematics illustrating recent understanding about the convergence between the two areas. Mathematicians Field and Golubitsky explain the relationship between chaos and symmetry, describing how chaotic process may eventually lead to symmetric patterns in a clear, understandable language and in color photographs reproducing computer images demonstrating the inherent pattern in apparent chaos. The authors compare these images with pictures from nature and art that, miraculously, mimic the computer patterns. Includes an appendix containing several BASIC programs enabling home computer owners to experiment with similar images. Annotation copyrighted by Book News, Inc., Portland, OR
The Symmetry Perspective
Author: Martin Golubitsky
Publisher: Birkhäuser
ISBN: 3034881673
Category : Technology & Engineering
Languages : en
Pages : 338
Book Description
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
Publisher: Birkhäuser
ISBN: 3034881673
Category : Technology & Engineering
Languages : en
Pages : 338
Book Description
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
Crystal and Dragon
Author: David Wade
Publisher: Inner Traditions / Bear & Co
ISBN: 9780892814046
Category : Art
Languages : en
Pages : 296
Book Description
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.
Publisher: Inner Traditions / Bear & Co
ISBN: 9780892814046
Category : Art
Languages : en
Pages : 296
Book Description
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.
Fearful Symmetry
Author: Ian Stewart
Publisher: Courier Corporation
ISBN: 0486477584
Category : Science
Languages : en
Pages : 326
Book Description
"From the shapes of clouds to dewdrops on a spider's web, this accessible book employs the mathematical concepts of symmetry to portray fascinating facets of the physical and biological world. More than 120 figures illustrate the interaction of symmetry with dynamics and the mathematical unity of nature's patterns"--
Publisher: Courier Corporation
ISBN: 0486477584
Category : Science
Languages : en
Pages : 326
Book Description
"From the shapes of clouds to dewdrops on a spider's web, this accessible book employs the mathematical concepts of symmetry to portray fascinating facets of the physical and biological world. More than 120 figures illustrate the interaction of symmetry with dynamics and the mathematical unity of nature's patterns"--
The Symmetry of Chaos
Author: Robert Gilmore
Publisher:
ISBN:
Category : Art
Languages : en
Pages : 618
Book Description
There is a tremendous fascination with chaos and fractals, about which picture books can be found on coffee tables everywhere. Chaos and fractals represent hands-on mathematics that is alive and changing. One can turn on a personal computer and create stunning mathematical images that no one has ever seen before. Chaos and fractals are part of dynamics, a larger subject that deals with change, with systems that evolve with time. Whether the system in question settles down to equilibrium, keeps repeating in cycles, or does something more complicated, it is dynamics that scientists and mathematicians use to analyze a system's behavior. Chaos is the term used to describe the apparently complex behavior of what we consider to be simple, well-behaved systems. Chaotic behavior, when looked at casually, looks erratic and almost random. The type of behavior that in the last 20 years has come to be called chaotic arises in very simple systems. In fact, these systems are essentially deterministic; that is, precise knowledge of the conditions of a system allow future behavior of the system to be predicted. The problem of chaos is to reconcile these apparently conflicting notions: randomness and predictability. Why have scientists, engineers, and mathematicians become intrigued by chaos? The answer to that question has two parts: (1) the study of chaos has provided new conceptual tools enabling scientists to categorize and understand complex behavior and (2) chaotic behavior seems to be universal - from electrical circuits to nerve cells. Chaos is about predictability in even the most unstable systems, and symmetry is a pattern of predictability - a conceptual tool to help understand complex behavior. The Symmetry of Chaos treats this interplay between chaos and symmetry. This graduate textbook in physics, applied mathematics, engineering, fluid dynamics, and chemistry is full of exciting new material, illustrated by hundreds of figures. Nonlinear dynamics and chaos are relatively young fields, and in addition to serving textbook markets, there is a strong interest among researchers in new results in the field. The authors are the foremost experts in this field, and this book should give a definitive account of this branch of dynamical systems theory.
Publisher:
ISBN:
Category : Art
Languages : en
Pages : 618
Book Description
There is a tremendous fascination with chaos and fractals, about which picture books can be found on coffee tables everywhere. Chaos and fractals represent hands-on mathematics that is alive and changing. One can turn on a personal computer and create stunning mathematical images that no one has ever seen before. Chaos and fractals are part of dynamics, a larger subject that deals with change, with systems that evolve with time. Whether the system in question settles down to equilibrium, keeps repeating in cycles, or does something more complicated, it is dynamics that scientists and mathematicians use to analyze a system's behavior. Chaos is the term used to describe the apparently complex behavior of what we consider to be simple, well-behaved systems. Chaotic behavior, when looked at casually, looks erratic and almost random. The type of behavior that in the last 20 years has come to be called chaotic arises in very simple systems. In fact, these systems are essentially deterministic; that is, precise knowledge of the conditions of a system allow future behavior of the system to be predicted. The problem of chaos is to reconcile these apparently conflicting notions: randomness and predictability. Why have scientists, engineers, and mathematicians become intrigued by chaos? The answer to that question has two parts: (1) the study of chaos has provided new conceptual tools enabling scientists to categorize and understand complex behavior and (2) chaotic behavior seems to be universal - from electrical circuits to nerve cells. Chaos is about predictability in even the most unstable systems, and symmetry is a pattern of predictability - a conceptual tool to help understand complex behavior. The Symmetry of Chaos treats this interplay between chaos and symmetry. This graduate textbook in physics, applied mathematics, engineering, fluid dynamics, and chemistry is full of exciting new material, illustrated by hundreds of figures. Nonlinear dynamics and chaos are relatively young fields, and in addition to serving textbook markets, there is a strong interest among researchers in new results in the field. The authors are the foremost experts in this field, and this book should give a definitive account of this branch of dynamical systems theory.
Quantum Signatures of Chaos
Author: Fritz Haake
Publisher: Springer Science & Business Media
ISBN: 3662045060
Category : Science
Languages : en
Pages : 491
Book Description
This classic text provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.
Publisher: Springer Science & Business Media
ISBN: 3662045060
Category : Science
Languages : en
Pages : 491
Book Description
This classic text provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.
Supersymmetry in Disorder and Chaos
Author: Konstantin Efetov
Publisher: Cambridge University Press
ISBN: 9780521663823
Category : Mathematics
Languages : en
Pages : 470
Book Description
This book provides a comprehensive treatment of the ideas and applications of supersymmetry.
Publisher: Cambridge University Press
ISBN: 9780521663823
Category : Mathematics
Languages : en
Pages : 470
Book Description
This book provides a comprehensive treatment of the ideas and applications of supersymmetry.
An Introduction to Dynamical Systems and Chaos
Author: G.C. Layek
Publisher: Springer
ISBN: 8132225562
Category : Mathematics
Languages : en
Pages : 632
Book Description
The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.
Publisher: Springer
ISBN: 8132225562
Category : Mathematics
Languages : en
Pages : 632
Book Description
The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.
Bigger Than Chaos
Author: Michael Strevens
Publisher: Harvard University Press
ISBN: 9780674010420
Category : Mathematics
Languages : en
Pages : 446
Book Description
Michael Strevens shows how simplicity can co-exist with the tangled interconnections within complex systems. By looking at the foundations of statistical reasoning about complex systems (gases, ecosystems and even social systems) he provides an understanding of how simplicity emerges from complexity.
Publisher: Harvard University Press
ISBN: 9780674010420
Category : Mathematics
Languages : en
Pages : 446
Book Description
Michael Strevens shows how simplicity can co-exist with the tangled interconnections within complex systems. By looking at the foundations of statistical reasoning about complex systems (gases, ecosystems and even social systems) he provides an understanding of how simplicity emerges from complexity.
Symmetry: A Very Short Introduction
Author: Ian Stewart
Publisher: OUP Oxford
ISBN: 0191652741
Category : Mathematics
Languages : en
Pages : 161
Book Description
In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Publisher: OUP Oxford
ISBN: 0191652741
Category : Mathematics
Languages : en
Pages : 161
Book Description
In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.