The 2, r- rule R30 Just How Random Is It

That neither complex nor random-like, behavior, need have a complex dynamical origin is well exemplified by the elementary one-dimensional class c3 rule R30, studied extensively by Wolfram in [wolf84c]. It is defined explicitly by 

Consider, for example, the space-time pattern resulting from application of to a single nonzero site value, shown in figure 3.30 We make the following observations  

The pattern consists of a curious mixture of regular behavior along the left-hand side and irregular behavior along the right-hand side, separated by a boundary moving towards the left at a speed of approximately sites/sec. 

The periodicity of the diagonal sequences on the left-hand side can be understood heuristically as follows. Any value situated at a distance d from the left-hand side boundary depend only on those values at distances d d because of the single nonzero site value seeding, all other values on which it could depend are identically equal to zero. The diagonal sequences along the left-hand side (LHS) therefore follow an effective rule, i,hs, which is a shifted version of equation 3.34  

The effective rule for the right-hand side (RHS) diagonal pattern is similarly a right-shifted version of equation 3.34  

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