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Symmetry in Chaos: A Search for Pattern in Mathematics, Art, and Nature Second Edition [Kõva köide]

  • Formaat: Hardback, 213 pages, kõrgus x laius x paksus: 229x152x19 mm, kaal: 1065 g, illustrations
  • Ilmumisaeg: 30-Apr-2009
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716721
  • ISBN-13: 9780898716726
Teised raamatud teemal:
  • Formaat: Hardback, 213 pages, kõrgus x laius x paksus: 229x152x19 mm, kaal: 1065 g, illustrations
  • Ilmumisaeg: 30-Apr-2009
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716721
  • ISBN-13: 9780898716726
Teised raamatud teemal:
Mathematical symmetry and chaos come together to form striking, beautiful colour images throughout this impressive work, which addresses how the dynamics of complexity can produce familiar universal patterns.

The book, a richly illustrated blend of mathematics and art, was widely hailed in publications as diverse as the New York Review of Books, Scientific American, and Science when first published in 1992. This much-anticipated second edition features many new illustrations and addresses the progress made in the mathematics and science underlying symmetric chaos in recent years; for example, the classifications of attractor symmetries and methods for determining the symmetries of higher dimensional analogues of images in the book. In particular, the concept of patterns on average and their occurrence in the Faraday fluid dynamics experiment is described in a revised introductory chapter.

The ideas addressed in this book have been featured at various conferences on intersections between art and mathematics, including the annual Bridges conference, and in lectures to art students at the University of Houston.

Arvustused

'An impressive and beautiful exploration of an impressive and beautiful area of mathematics - the interplay between order and chaos. The images are breathtaking, the mathematics fundamental. Symmetry in Chaos is an important book, a work of art, and a joy to read.' Ian Stewart, author of Why Beauty is Truth 'A classic in the interdisciplinary field of art and mathematics, this very well written book takes the ingenious idea of combining symmetry with chaos to construct stunning images that anyone can enjoy, in particular mathematicians, who can also appreciate the underlying mathematics. Beautiful art cannot be the result of just clever computer graphics. The artist must also have a keen sense of color and that intangible artistic sensibility, which is present in Symmetry in Chaos. Anyone interested in the relationship of art and mathematics should read this book.' Nat Friedman, Director, International Society of the Arts, Mathematics and Architecture

Introduction to Symmetry and Chaos
1(34)
Symmetry
3(7)
Chaos
10(1)
Determinism
10(2)
Sensitive dependence
12(1)
Rules
13(2)
Pixel rules
15(2)
Coloring by number
17(2)
Arithmetic rules
19(2)
Strange attractors
21(1)
Statistics
22(1)
Symmetry on average
23(1)
What, how, and why?
24(4)
Patterns and turbulence
28(2)
The Faraday experiment
30(2)
Some further speculation
32(3)
Planar Symmetries
35(20)
Types of symmetric pictures
36(1)
Groups
37(1)
Symmetries of regular figures
38(6)
The wallpaper groups
44(3)
Coloring and interlacing
47(8)
Patterns Everywhere
55(34)
Icons with pentagonal symmetry
57(2)
Icons with different symmetries
59(15)
Tilings
74(11)
Islamic art
85(4)
Chaos and Symmetry Creation
89(14)
The logistic map
91(3)
The period-doubling cascade
94(3)
Symmetric maps on the line
97(1)
Symmetry creation
98(3)
Chaotic trains
101(2)
Symmetric Icons
103(26)
Mappings with dihedral symmetry
104(1)
An illustration of chaos
105(3)
Numerology
108(8)
Geometry of the complex numbers
116(3)
Dihedral symmetry
119(1)
The dihedral logistic mappings
119(5)
Symmetry creation in the plane
124(5)
Quilts
129(10)
Repeating patterns
131(1)
The square lattice
132(1)
Seams
133(1)
Internal symmetry
134(1)
The hexagonal lattice
135(1)
Less internal symmetry
136(3)
Symmetric Fractals
139(32)
Fractals
141(1)
The Sierpinski triangle
142(2)
Probability and random numbers
144(2)
Probability one
146(1)
Sierpinski polygons
147(3)
Affine linear maps
150(1)
Contractions
151(1)
Iterated function systems and fractals
152(1)
Strict fractals and overlaid fractals
153(1)
Two basic theorems
154(4)
The Sierpinski square
158(1)
Symmetric fractals
158(2)
The Sierpinski triangle is symmetric
160(1)
Structure on all scales
161(1)
More examples
161(10)
Appendix A Picture Parameters
171(6)
Symmetric icons
171(2)
Symmetric quilts
173(1)
Symmetric fractals
174(3)
Appendix B Icon Mappings
177(6)
Symmetry on the line
177(2)
Dn equivariants
179(1)
Zn equivariants
180(3)
Appendix C Planar Lattices
183(12)
Action of the holohedry on the torus
185(1)
Mappings on the torus
186(1)
Symmetric torus mappings
187(1)
Fourier expansions of £-periodic mappings
188(2)
The quilt mappings
190(2)
Quilts with cyclic symmetry
192(3)
Bibliography 195(2)
Index 197
Michael Field has been a Professor at the University of Houston since 1992. He received his PhD in mathematics from the University of Warwick in 1970. His research interests include ergodic theory, coupled cell systems, the geometric theory of dynamical systems with symmetry and the mechanisms whereby symmetry can lead to complex dynamics in low dimensional systems. Martin Golubitsky is Distinguished Professor of Mathematics and Physical Sciences at the Ohio State University, where he serves as Director of the Mathematical Biosciences Institute. He received his PhD in Mathematics from M.I.T. in 1970 and has been Professor of Mathematics at Arizona State University (1979-83) and Cullen Distinguished Professor of Mathematics at the University of Houston (1983-2008). Dr Golubitsky works in the fields of nonlinear dynamics and bifurcation theory studying the role of symmetry in the formation of patterns in physical systems and the role of network architecture in the dynamics of coupled systems. He has co-authored four graduate texts, one undergraduate text, two nontechnical trade books, and over 100 research papers.