Locating Self-Organization at the Edge of Chaos
Langton  attempted to parametrically characterize subspaces of cellular automata (CA) rules that determine trajectories of the automata that are not quite chaotic but still sufficiently complex to be able to carry out computation. As the number of available local states and neighborhood size increases it is difficult to sharply recognize regular structure in either the subspace of rules or the corresponding parameter values. In-depth re-examination of Langton’s parameterization of the CA-rule space by Mitchell, Hraber and Crutchfield  casts doubt on the utility of Langton’s original parameterization but leaves open the question of whether interesting emergent structure in the trajectories of CAs capable of supporting computation is associated with CA-rules located at or near phase transitions in the rule space.
KeywordsLyapunov Exponent Cellular Automaton Topological Entropy Large Lyapunov Exponent Fibonacci Number
Unable to display preview. Download preview PDF.
- Blair, H.A., F. Dushin, D.W. Jakel, A.J. Rivera, and M. Sezgin “Continuous models of computation for logic programs: importing continuous mathematics into logic programming’s algorithmic foundations”, The Logic Programming Paradigm (K.R. Apt, V.W. Marek, M. Truszczynski, and D.S. Warren eds.) Springer (1999), 231–255.Google Scholar
- Kruse, R., J. Gebhardt, and F. Klawonn, Foundations of Fuzzy Systems, Wiley (1994).Google Scholar