Phase transition in an elementary probabilistic cellular automaton
Cellular automata exhibit a large variety of dynamical behaviors, from fixed-point convergence and periodic motion to spatio-temporal chaos. By introducing probabilistic interactions, and regarding the asymptotic density Φ of non-quiescent cell states as an order parameter, phase transitions may be identified from a quiescent phase with Φ = 0 to a chaotic phase with non-zero Φ. We consider an elementary one-dimensional probabilistic cellular automaton (PCA) with deterministic limits given by the quiescent rule 0, the rule 72 that evolves into a non-trivial fixed point, and the chaotic rules 18 and 90. Despite the simplicity of the rules, the PCA shows a surprising number of transition phenomena. We identify ‘second-order’ phase transitions from Φ = 0 to Φ > 0 with static and dynamic exponents that differ from those of directed percolation. Moreover, we find that the non-trivial fixed-point rule 72 is a singular point in PCA space.
Year of publication: |
1997
|
---|---|
Authors: | Petersen, Niels K. ; Alstrøm, Preben |
Published in: |
Physica A: Statistical Mechanics and its Applications. - Elsevier, ISSN 0378-4371. - Vol. 235.1997, 3, p. 473-485
|
Publisher: |
Elsevier |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
“Thermodynamical formalism” for an infinite hierarchy of fractal resistor networks
Alstrøm, Preben, (1988)
-
Reliability of neural encoding
Alstrøm, Preben, (2002)
-
Randløv, Jette, (2001)
- More ...