Showing papers by "Stephen Wolfram published in 1983"
TL;DR: Analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors.
Abstract: Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of "elementary" cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate self-similar patterns with fractal dimensions \ensuremath{\simeq} 1.59 or \ensuremath{\simeq} 1.69. With "random" initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed.
2,860 citations
01 Jan 1983
TL;DR: In this article, it was shown that all one-dimensional cellular automata fall into four distinct universality classes: limit points, limit cycles, chaotic attractors, and limit cycles.
Abstract: Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.
1,709 citations
TL;DR: In this article, the energy and entropy of quantized fields in cavities with a variety of forms are calculated. But the authors do not consider the possibility of negative mass systems.
402 citations
TL;DR: In this paper, a QCD model for e+e− annihilation is presented, and its consequences are compared with experimental data, which involves production of a shower of partons described by a simple approximation to QCD perturbation theory, and decay of colour singlet clusters of produced partons into hadrons through a simple phase space process.
127 citations
TL;DR: In this article, the behavior of a charged scalar field in an external electric field is discussed, and the authors present a self-consistent semiclassical procedure to calculate vacuum polarization.
68 citations
TL;DR: In this article, the existence of large numbers of very massive particles in the very early universe has been investigated, and it has been shown that their presence could completely change the equation of state and expansion rate of the early universe, and could have important effects on baryon-number generation.
Abstract: Several theoretical principles suggest the existence of large numbers of very massive particles. Such particles have negligible effect in the present universe, but may have been important in the very early universe. It is shown that under some circumstances their presence could completely change the equation of state and expansion rate of the very early universe, and could have important effects on baryon-number generation. Possible cosmological constraints on the complexity of grand unified gauge models are discussed.
7 citations