Chapter 8: Implications for Everyday Systems

Section 7: Biological Pigmentation Patterns

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]&]

From Stephen Wolfram: A New Kind of Science [citation]