Implementation [of patterning model]

Given a 2D array of values a and a list of weights w, each step in the evolution of the system corresponds to

WeightedStep[w_List, a_] := Map[If[# > 0, 1, 0]&, Sum[w〚1 + i〛 Apply[Plus, Map[RotateLeft[a, #]&, Layer[i]]], {i, 0, Length[w] - 1}], {2}]

Layer[n_] := Layer[n] = Select[Flatten[Table[{i, j}, {i, -n, n}, {j, -n, n}],1], MemberQ[#, n| - n]&]