A Stochastic Version of Conways Life Rule

An early study of a stochastic CA system was performed by Schulman and Seiden in 1978 using a generalized version of Conway s Life rule [schul78]. Though there was little follow-on effort stemming directly from this particular paper, the study nonetheless serves as a useful prototype for later analyses. The manner in which Schulman and Seiden incorporate site-site correlations into their calculations, for example, bears some resemblance to Gutowitz, et.ai. s Local Structure Theory, developed about a decade later (see section 5.3). In this section, we outline some of their methodology and results. 

We begin by recalling that Conway s original deterministic rule is an outer-totalistic (code OT224) k = 2 rule defined on the two-dimensional Moore neighborhood  

To be more precise, P is the probability that a site having exactly k living (i.e. (7=1) neighbors either survives a = S and the given site had previously been alive) or is born (a = P and the given site had previously been dead). Conway s deterministic rule, of course, is reproduced by setting Pg = Sk,3 and P = Sk,2 + 6k,3- 

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