Implementation [of causal networks]

Given a list of successive positions of the active cell, as from Map[Last, MAEvolveList[rule, init, t]] (see page 887), the network can be generated using

MAToNet[list_] := Module[{u, j, k}, u[_] = ∞; Reverse[Table[j = list〚i〛; k = {u[j - 1], u[j], u[j + 1]}; u[j - 1] = u[j] = u[j + 1] = i; i  k, {i, Length[list], 1, -1}]]]

where nodes not yet found by explicit evolution are indicated by ∞.