The interdependency between cells at the stationary distribution as function of distance. Note that the “stationary distribution” in this case is computed as follows: the system is initialized with a uniform distribution (i.e. purely random independent bits), and is evolved following the rule of the automaton until some distribution re-occurs.

In this case, the interdependency between the cells \(X^8_t\) and \(X^k_t\) is given by the mutual information \(I(X^8_t;X^k_t)\), where \(t\) is the number of steps required to reach the stationary distribution. The choice of the mutual information over traditional metrics of linear correlation (e.g. the Pearson Coefficient) is for taking into account non-linear interdependencies as well.

In this case, the interdependency between the cells \(X^8_t\) and \(X^k_t\) is given by the mutual information \(I(X^8_t;X^k_t)\), where \(t\) is the number of steps required to reach the stationary distribution. The choice of the mutual information over traditional metrics of linear correlation (e.g. the Pearson Coefficient) is for taking into account non-linear interdependencies as well.