Author: Leon O Chua
Publisher: World Scientific
Release Date: 2012-03-13
This penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence. Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the super string S, which contains all random bit strings of finite length as sub-strings. As an illustration of the mathematical subtlety of this amazing discrete testing signal, the super string S is used to prove mathematically, in a trivial and transparent way, that rule 170 is as chaotic as a coin toss. Yet another unexpected new result, among many others, is the derivation of an explicit basin tree generation formula which provides an analytical relationship between the basin trees of globally-equivalent local rules. This formula allows the symbolic, rather than numerical, generation of the time evolution of any local rule corresponding to any initial bit-string configuration, from one of the 88 globally-equivalent local rules. But perhaps the most provocative idea is the proposal for adopting rule 137, over its three globally-equivalent siblings, including the heretofore more well-known rule 110, as the prototypical universal Turing machine. Contents:Period-2 Rules:Recap of Period-2 RulesBasin Tree DiagramsRobust ω-Limit Orbits of Local Rules Belonging to Group 2Quasi Global-EquivalenceSuper String S and Super Decimal xSConcluding RemarksPeriod-3, Period-6, and Permutive Rules:List of the 88 Minimal Equivalence RulesBasin Tree Diagrams, Omega-Limit Orbits and Time-τ Characteristic Function of Rules from Group 3Robust ω-Limit Orbits of Rules from Group 3Permutive RulesConcluding Remarks Readership: Graduate students, researchers and academics interested in nonlinear dynamics, computer science and complexity theory. Keywords:Cellular Automata;CNN;Chua;Wolfram;Wolfram's New Kind of Science;Computer Science;Complexity;Nonlinear Dynamics
Author: Leon O. Chua
Publisher: World Scientific Publishing Company Incorporated
Release Date: 2009
Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli ??-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and hyper Bernoulli wave dynamics. Explicit global state transition formulas derived for rules 60, 90, 105, and 150 reveal a new scale-free phenomenon. The most surprising new result unveiled in this volume is the “Isle of Eden” found hidden in most (almost 90%) of the 256 local rules. Readers are challenged to hunt for long-period, isolated Isles of Eden. These are rare gems waiting to be discovered.
Author: Paolo Grigolini
Publisher: World Scientific
Release Date: 2011
Genre: Chaotic behavior in systems
This invaluable book captures the proceedings of a workshop that brought together a group of distinguished scientists from a variety of disciplines to discuss how networking influences decision making. The individual lectures interconnect psychological testing, the modeling of neuron networks and brain dynamics to the transport of information within and between complex networks. Of particular importance was the introduction of a new principle that governs how complex networks talk to one another OCo the Principle of Complexity Management (PCM). PCM establishes that the transfer of information from a stimulating complex network to a responding complex network is determined by how the complexity indices of the two networks are related. The response runs the gamut from being independent of the perturbation to being completely dominated by it, depending on the complexity mismatch.
Author: Sun I. Kim
Publisher: Springer Science & Business Media
Release Date: 2007-07-05
Genre: Technology & Engineering
These proceedings of the World Congress 2006, the fourteenth conference in this series, offer a strong scientific program covering a wide range of issues and challenges which are currently present in Medical physics and Biomedical Engineering. About 2,500 peer reviewed contributions are presented in a six volume book, comprising 25 tracks, joint conferences and symposia, and including invited contributions from well known researchers in this field.