Computation and phase transitions

Langton was able to provide a tentative answer to his question - at least within the somewhat more limited realm of the complex dynamics of CA - by examining the behavior of the entire rule space of elementary one-dimensional CA rules as parameterized by a single parameter A (see section 3.2.1). Given a rule 4 , A is defined to be the fraction of entries in the rule table for f) get mapped to a non-zero value [langOO]. 

If a fundamental equivalence between the dynamics of phase transitions and information processing along the lines suggested by Langton really exists, it would also lend support to the Church-l iring hypothesis [lang92]  

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