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Volume IV continues the author’s odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing the fractal properties of characteristic functions, as well as explicit formulas for generating colorful and pedagogically revealing isomorphic basin tree diagrams.
For many centuries, scientists have investigated the “fearful symmetry” that seemed to underlie the Universe. But increasingly, it looks as though life is the result of cosmic asymmetry, and scientists are now preparing to uncover the asymmetries at the heart of the Big Bang. This text follows the trail, from subtle asymmetries in Nature to the mysterious Higg’s boson that scientists now believe may hold the key to the birth of the Universe itself.
"Introducing Chaos" explains how chaos makes its presence felt in many varieties of event, from the fluctuation of animal populations to the ups and downs of the stock market. It also examines the roots of chaos in modern mathematics and physics, and explores the relationship between chaos and complexity, the new unifying theory which suggests that all complex systems evolve from a few simple rules.This is an accessible introduction to an astonishing and controversial theory that could dramatically change our view of the natural world and our place in a turbulent universe.
Imagine trying to understand a stained glass window by breaking it into pieces and examining it one shard at a time. While you could probably learn a lot about each piece, you would have no idea about what the entire picture looks like. This is reductionism—the idea that to understand the world we only need to study its pieces—and it is how most social scientists approach their work.In A Crude Look at the Whole, social scientist and economist John H. Miller shows why we need to start looking at whole pictures.
The topics presented in this volume include: critical behavior as explained by the non-perturbative renormalization group, critical dynamics, a spacetime approach to phase transitions, self-organized criticality, and exactly solvable models of phase transitions in strongly correlated systems.
Piecewise constant systems exist in widely expanded areas such as engineering, physics, and mathematics. Extraordinary and complex characteristics of piecewise constant systems have been reported in recent years. This book provides the methodologies for analyzing and assessing nonlinear piecewise constant systems on a theoretically and practically sound basis.
This book provides a compilation of mathematical-computational tools that are used to analyze experimental data. The techniques presented are those that have been most widely and successfully applied to the analysis of physiological systems, and address issues such as randomness, determinism, dimension, and nonlinearity.
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