Chapter 5: Two Dimensions and Beyond

Section 4: Substitution Systems and Fractals

Implementation [of 2D substitution systems]

With the rule on page 187 given for example by {1->{{1, 0}, {1, 1}}, 0->{{0, 0}, {0, 0}}} the result of t steps in the evolution of a 2D substitution system from a initial condition such as {{1}} is given by

SS2DEvolve[rule_, init_, t_] := Nest[Flatten2D[# /. rule]&, init, t] Flatten2D[list_] := Apply[Join, Map[MapThread[Join, #]&, list]]

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