FAMap[rule_,s0_,n_,k_:2]:=Table[{i,FromDigits[FAStep[rule,s0,IntegerDigits[i,k,n]],k]},{i,0,k^n-1}]
FAMapMatrix[rule_,s0_,n_,k_:2]:=Normal[SparseArray[((#+1)1)&/@FAMap[rule,s0,n],{k^n,k^n}]]