Universal Cellular Automata and Class 4

Dhar, Avinash ; Lakdawala, Porus ; Mandal, Gautam ; Wadia, Spenta R (1995) Universal Cellular Automata and Class 4 Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 51 . p. 3032. ISSN 1539-3755

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Official URL: http://pre.aps.org/


Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long transients). These properties of Class 4 CA's has led to the conjecture that Class 4 rules are Universal Turing machines i.e. they are bases for computational universality. We describe an embedding of a ``small'' universal Turing machine due to Minsky, into a cellular automaton rule-table. This produces a collection of (k=18,r=1) cellular automata, all of which are computationally universal. However, we observe that these rules are distributed amongst the various Wolfram classes. More precisely, we show that the identification of the Wolfram class depends crucially on the set of initial conditions used to simulate the given CA. This work, among others, indicates that a description of complex systems and information dynamics may need a new framework for non-equilibrium statistical mechanics.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:92197
Deposited On:04 Jun 2012 06:31
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