# Search Results for "a-nonlinear-dynamics-perspective-of-wolfram-s-new-kind-of-science"

## A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science

**Author**: Leon O. Chua**Publisher:**World Scientific**ISBN:**9814317306**Category:**Science**Page:**392**View:**3028

Annotation This text introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. It provides an analysis, and classification of the empirical results presented in Wolfram's 'New Kind of Science'.

## A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science

*(Volume VI)*

**Author**: Leon O Chua**Publisher:**World Scientific**ISBN:**9814460893**Category:**Computers**Page:**580**View:**9871

This invaluable volume ends the quest to uncover the secret recipes for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor (i.e. after the transients had disappeared) is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables. As befitting the contents aimed at school children, it was found pedagogically appealing to code each truth table by coloring each of the 8 vertices of a cubical graph in red (for binary state 1), or blue (for binary state 0), forming a toy universe of 256 Boolean cubes, each bearing a different vertex color combination. The corresponding collection of 256 distinct Boolean cubes are then segegrated logically into 6 distinct groups where members from each group share certain common dynamics which allow the long-term evolution of the color configuration of each bit string, of arbitrary length, to be predicted painlessly, via a toy-like gaming procedure, without involving any calculation. In particular, the evolution of any bit string bearing any initial color configuration which resides in any one of the possibly many distinct attractors, can be systematically predicted, by school children who are yet to learn arithmetic, via a simple recipe, for any Boolean cube belonging to group 1, 2, 3, or 4. The simple recipe for predicting the time-asymptotic behaviors of Boolean cubes belonging to groups 1, 2, and 3 has been covered in Vols. I, II, ..., V. This final volume continues the recipe for each of the 108, out of 256, local rules, dubbed the Bernoulli rules, belonging to group 4. Here, for almost half of the toy universe, surprisingly simple recipes involving only the following three pieces of information are derived in Vol. VI; namely, a positive integer τ, a positive, or negative, integer σ, and a sign parameter β > 0, or β < 0. In particular, given any color configuration belonging to an attractor of any one of the 108 Boolean cubes from group 4, any child can predict the color configuration after τ generations, without any computation, by merely shifting each cell σ bits to the left (resp. right) if σ > 0 (resp. σ < 0), and then change the color of each cell if β < 0. As in the five prior volumes, Vol. VI also contains simple recipes which are, in fact, general and original results from the abstract theory of 1-dimensional cellular automata. Indeed, both children and experts from cellular automata will find this volume to be as deep, refreshing, and entertaining, as the previous volumes. Contents:Bernoulli στ-Shift Rules:IntroductionBasin Tree Diagrams, Omega-Limit Orbits and Space-Time PatternsRobust and Nonrobust ω-Limit Orbits of Rules from Group 4Concluding RemarksMore Bernoulli στ-Shift Rules:IntroductionBernoulli στ-Shift RulesRobust and Nonrobust ω-Limit Orbits of Rules from Group 4Summary of Elementary 1D Cellular AutomataConcluding RemarksRemembrance of Things Past:Vignettes from Volume IVignettes from Volume IIVignettes from Volume IIIVignettes from Volume IVVignettes from Volume VVignettes from Volume VIVignettes of Metaphors from Biology, Cosmology, Physics, etc.Vignettes of 256 Boolean Cubes Readership: Students, researchers, academics as well as laymen 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

## Cellular Automata

*8th International Conference on Cellular Automata for Research and Industry, ACRI 2008, Yokohama, Japan, September 23-26, 2008, Proceedings*

**Author**: International Conference on Cellular Automata for Research and Industry**Publisher:**Springer Science & Business Media**ISBN:**3540799915**Category:**Computers**Page:**577**View:**7861

This volume constitutes the proceedings of the 8th International Conference on Cellular Automata for Research and Industry, ACRI 2008, which took place in Yokohama, Japan, September 23-26,2008. The conference, which was organized by YokohamaNational University, was the eighth in a series of conferences in- guratedin1994inRende, Italy, andfollowedbyACRI1996inMilan, Italy, ACRI 1998in Trieste, Italy, ACRI 2000in Karlsruhe, Germany, ACRI 2002in Geneva, Switzerland, ACRI2004inAmsterdam, TheNetherlandsandACRI2006inP- pignan, France. The ACRI conference has been traditionally focused on challenging problems and new research not only in theoretical but application aspects of cellular - tomata, including cellular automata tools and computational sciences. It is also concerned with applications and solutions of problems from the ?elds of physics, engineering, environmentscience, socialscienceandlifesciences.Itsprimarygoal istodiscussproblemsfromavarietyofscienti?c?elds, toidentify newissuesand to enlarge the research ?elds of cellular automata. Since its inception, the ACRI conference has attracted an ever-growing community and has raised knowledge andinterestinthe studyofcellularautomataforbothnewentrantsintothe ?eld aswellasresearchersalreadyworkingonparticularaspectsofcellularautomata. First invented by von Neumann, cellular automata models have been po- larizedandinvestigatedinmanyareasduring thelastfew decades.They provide a mathematically rigorous framework for a class of discrete dynamical systems that allow complex, unpredictable behavior to emerge from the deterministic - calinteractionsofmanysimple components operatinginparallelanddistributed manner.

## Collective Dynamics of Nonlinear and Disordered Systems

**Author**: Günter Radons,Wolfram Just**Publisher:**Springer Science & Business Media**ISBN:**9783540213833**Category:**Science**Page:**378**View:**8009

Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

## Structural Dynamics of Earthquake Engineering

*Theory and Application Using Mathematica and Matlab*

**Author**: S Rajasekaran**Publisher:**Elsevier**ISBN:**1845695739**Category:**Technology & Engineering**Page:**896**View:**9550

Given the risk of earthquakes in many countries, knowing how structural dynamics can be applied to earthquake engineering of structures, both in theory and practice, is a vital aspect of improving the safety of buildings and structures. It can also reduce the number of deaths and injuries and the amount of property damage. The book begins by discussing free vibration of single-degree-of-freedom (SDOF) systems, both damped and undamped, and forced vibration (harmonic force) of SDOF systems. Response to periodic dynamic loadings and impulse loads are also discussed, as are two degrees of freedom linear system response methods and free vibration of multiple degrees of freedom. Further chapters cover time history response by natural mode superposition, numerical solution methods for natural frequencies and mode shapes and differential quadrature, transformation and Finite Element methods for vibration problems. Other topics such as earthquake ground motion, response spectra and earthquake analysis of linear systems are discussed. Structural dynamics of earthquake engineering: theory and application using Mathematica and Matlab provides civil and structural engineers and students with an understanding of the dynamic response of structures to earthquakes and the common analysis techniques employed to evaluate these responses. Worked examples in Mathematica and Matlab are given. Explains the dynamic response of structures to earthquakes including periodic dynamic loadings and impulse loads Examines common analysis techniques such as natural mode superposition, the finite element method and numerical solutions Investigates this important topic in terms of both theory and practise with the inclusion of practical exercise and diagrams

## Celestial Encounters

*The Origins of Chaos and Stability*

**Author**: Florin Diacu,Philip Holmes**Publisher:**Princeton University Press**ISBN:**9780691005454**Category:**Mathematics**Page:**256**View:**8007

Celestial Encounters traces the history of attempts to solve the problem of celestial mechanics first posited in Isaac Newton's Principia in 1686. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it. 23 halftones. 64 line illustrations.

## Pharmaco-Complexity

*Non-Linear Phenomena and Drug Product Development*

**Author**: Anthony J. Hickey,Hugh D.C. Smyth**Publisher:**Springer Science & Business Media**ISBN:**9781441978561**Category:**Medical**Page:**71**View:**2857

The historical approach to the interpretation of physical, chemical and biological phenomena has been to consider relationships with causative factors that can be reduced to linearity allowing simple and direct interpretation. However, it is increasingly evident that there is often more information in the data than linear interpretations allow. The current capacity for computers to assist in identifying non-linear relationships allows greater interpretation of data which illuminates the phenomena allowing the information to be translated into knowledge that can be used wisely to promote various desirable pharmaceutical outcomes. This short volume is intended to stimulate the reader to contemplate research and development areas in which the data might be more accurately interpreted to allow greater understanding and ultimately control of the pharmaceutically complex phenomena.

## Solving Nonlinear Partial Differential Equations with Maple and Mathematica

**Author**: Inna Shingareva,Carlos Lizárraga-Celaya**Publisher:**Springer Science & Business Media**ISBN:**370910517X**Category:**Mathematics**Page:**357**View:**3826

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

## The Mathematics of Marriage

*Dynamic Nonlinear Models*

**Author**: John Mordechai Gottman**Publisher:**MIT Press**ISBN:**9780262250450**Category:**Psychology**Page:**500**View:**2389

Divorce rates are at an all-time high. But without a theoretical understanding of the processes related to marital stability and dissolution, it is difficult to design and evaluate new marriage interventions. The Mathematics of Marriage provides the foundation for a scientific theory of marital relations. The book does not rely on metaphors, but develops and applies a mathematical model using difference equations. The work is the fulfillment of the goal to build a mathematical framework for the general system theory of families first suggested by Ludwig Von Bertalanffy in the 1960s.The book also presents a complete introduction to the mathematics involved in theory building and testing, and details the development of experiments and models. In one "marriage experiment," for example, the authors explored the effects of lowering or raising a couple's heart rates. Armed with their mathematical model, they were able to do real experiments to determine which processes were affected by their interventions.Applying ideas such as phase space, null clines, influence functions, inertia, and uninfluenced and influenced stable steady states (attractors), the authors show how other researchers can use the methods to weigh their own data with positive and negative weights. While the focus is on modeling marriage, the techniques can be applied to other types of psychological phenomena as well.