Showing papers by "James P. Crutchfield published in 1993"
Journal Article•
TL;DR: Mitchell et al. as discussed by the authors presented results from an experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task.
Abstract: Author(s): Mitchell, Melanie; Hraber, Peter; Crutchfield, James P | Abstract: We present results from an experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton's lambda parameter (Langton, 1990), and interpreted the results of his experiment as giving evidence for the following two hypotheses: (1) CA rules able to perform complex computations are most likely to be found near ``critical'' lambda values, which have been claimed to correlate with a phase transition between ordered and chaotic behavioral regimes for CA; (2) When CA rules are evolved to perform a complex computation, evolution will tend to select rules with lambda values close to the critical values. Our experiment produced very different results, and we suggest that the interpretation of the original results is not correct. We also review and discuss issues related to lambda, dynamical-behavior classes, and computation in CA. The main constructive results of our study are identifying the emergence and competition of computational strategies and analyzing the central role of symmetries in an evolutionary system. In particular, we demonstrate how symmetry breaking can impede the evolution toward higher computational capability.
474 citations
TL;DR: The decompostion technique is illustrated by analyzing a binary, range-2 cellular automaton having two invariant chaotic domains of different complexities and entropies, and how to construct a finite-state transducer that performs nonlinear spatial filtering such that the resulting space-time patterns reveal the domains and the intervening walls and dislocations.
118 citations
TL;DR: In this paper, the authors present evidence that the quasi-periodic oscillations (QPO) and very low frequency noise (VLFN) characteristic of many accretion sources are different aspects of the same physical process.
Abstract: We present evidence that the quasi-periodic oscillations (QPO) and very low frequency noise (VLFN) characteristic of many accretion sources are different aspects of the same physical process. We analyzed a long, high time resolution EXOSAT observation of the low-mass X-ray binary (LMXB) Sco X-1. The X-ray luminosity varies stochastically on time scales from milliseconds to hours. The nature of this variability - as quantified with both power spectrum analysis and a new wavelet technique, the scalegram - agrees well with the dripping handrail accretion model, a simple dynamical system which exhibits transient chaos. In this model both the QPO and VLFN are produced by radiation from blobs with a wide size distribution, resulting from accretion and subsequent diffusion of hot gas, the density of which is limited by an unspecified instability to lie below a threshold.
82 citations
Posted Content•
TL;DR: In this article, the authors present results from an experiment similar to the one described in Packard88, that was cited there as evidence for the hypothesis that rules capable of performing complex computations are most likely to be found at a phase transition between ordered and chaotic behavioral regimes for CA (the ''edge of chaos'').
Abstract: In this paper we review previous work and present new work concerning the relationship between dynamical systems theory and computation. In particular, we review work by Langton \cite{Langton90} and Packard \cite{Packard88} on the relationship between dynamical behavior and computational capability in cellular automata (CA). We present results from an experiment similar to the one described in \cite{Packard88}, that was cited there as evidence for the hypothesis that rules capable of performing complex computations are most likely to be found at a phase transition between ordered and chaotic behavioral regimes for CA (the ``edge of chaos''). Our experiment produced very different results from the original experiment, and we suggest that the interpretation of the original results is not correct. We conclude by discussing general issues related to dynamics, computation, and the ``edge of chaos'' in cellular automata.
39 citations
TL;DR: It is overwhelmingly likely that the recently proposed attractor-basin portrait captures the CA's qualitative dynamics, which mimic the behavior of typical lattices throughout their evolution until finite-size effects appear.
Abstract: The temporal decay of an attractor’s vicinity for a domain‐wall dominated cellular automaton (CA) is studied. Using selected initial pattern ensembles, state space structures in this high‐dimensional nonlinear spatial system can be identified via the resulting decay to its attractors. Considered over a range of lattice sizes, the decay behavior falls into three main classes, each of which shows a characteristic profile. The first consists of even‐size lattices showing a decelerating decay to small nonattracted ensemble fractions. The second class, also for even lattices, is a catastrophic decay to very small or vanishing nonattracted fractions. The third class also shows catastrophic decay and contains all odd‐size lattices. Stochastic models are constructed that mimic the behavior of typical lattices throughout their evolution until finite‐size effects appear. Weak additive noise causes all states on all lattices to fall into the attractor. In the end we find it overwhelmingly likely that the recently proposed attractor‐basin portrait captures the CA’s qualitative dynamics.
30 citations
Posted Content•
TL;DR: An experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata to perform a particular computational task, demonstrates how symmetry breaking can impede the evolution toward higher computational capability.
Abstract: We present results from an experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton's lambda parameter (Langton, 1990), and interpreted the results of his experiment as giving evidence for the following two hypotheses: (1) CA rules able to perform complex computations are most likely to be found near ``critical'' lambda values, which have been claimed to correlate with a phase transition between ordered and chaotic behavioral regimes for CA; (2) When CA rules are evolved to perform a complex computation, evolution will tend to select rules with lambda values close to the critical values. Our experiment produced very different results, and we suggest that the interpretation of the original results is not correct. We also review and discuss issues related to lambda, dynamical-behavior classes, and computation in CA. The main constructive results of our study are identifying the emergence and competition of computational strategies and analyzing the central role of symmetries in an evolutionary system. In particular, we demonstrate how symmetry breaking can impede the evolution toward higher computational capability.
17 citations