## Symmetry and Complexity: The Spirit and Beauty of Nonlinear ScienceCosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences, philosophy and the arts. With many diagrams and pictures, this book illustrates the spirit and beauty of nonlinear science. In the complex world of globalization, it strongly argues for unity in diversity. |

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Symmetry and Complexity: The Spirit and Beauty of Nonlinear Science Klaus Mainzer Limited preview - 2005 |

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3-dimensional According atoms attractors behavior bifurcation biological brain cells cellular automata chaos chaotic characterized chemical complex dynamical complex systems computational concept coordinates corresponding cosmic deﬁned deﬁnition diﬀerent diﬀerential equations dynamical systems economic eﬀect electromagnetic electrons elementary particles elements emergence energy entropy equilibrium Euclidean evolution example ﬁeld ﬁgures ﬁnal ﬁnd ﬁnite ﬁrst ﬂuctuations ﬂuid forces fractal frieze groups function geometry global gravitation human inﬁnite inﬂuence invariance Julia sets laws local symmetry macroscopic Mainzer mathematical metric models modern molecular molecules motion Nash equilibrium nature neural neurons nonlinear dynamics orbitals order parameters organisms patterns phase transitions philosophy physical plane Platonic player polygons possible principle processes proportions Pythagorean quantum mechanics reﬂection regular rotation scientiﬁc self-organization sequence social space space-time spatial speciﬁc Springer structures suﬃcient superstring theories supersymmetry symmetry and complexity symmetry breaking theory tion transformations Turing uniﬁcation uniﬁed universe weak interaction

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Page 13 - Dissipative selforganization means the phase transition of irreversible structures far from thermal equilibrium. Macroscopic patterns arise from the complex nonlinear cooperation of microscopic elements when the energetic interaction of the dissipative ('open') system with its environment reaches some critical value.