Sequential substitution systems [from cellular automata]

Given a sequential substitution system with rules in the form used on page 893, the rules for a cellular automaton which emulates it can be obtained from

SSSToCA[rules_] := Flatten[{{v[_, _, _], u, _}  u, {_, v[rn_, x_, _], u}  r[rn + 1, x], {_, v[_, x_, _], _}  x, MapIndexed[With[{r n = #2〚1〛, rs = #1〚1〛, rr = #1〚2〛}, {If[Length[rs]  1, {u, r[rn, First[rs]], _}  q[0, rr], {u, r[rn, First[rs]], _}  v[rn, First[rs], Take[rs, 1]]], {u, r[rn, x_], _}  v[rn, x, {}], {v[rn, _, Drop[rs, -1]], Last[rs], _}  q[Length[rs] - 1, rr], Table[{v[rn, _, Flatten[{___, Take[rs, i - 1]}]], rs〚i〛, _}  v[rn, rs〚i〛, Take[rs, i]], {i, Length[rs] - 1, 1, -1}], {v[rn, _, _], y_, _}  v[rn, y, {}]}] & , rules /. s  List], {_, q[0, {x__, _}], _}  q[0, {x}], {_, q[0, {x_}], _}  r[1, x], {_, q[0, {}], x_}  r[1, x], {_, q[_, {___, x_}], _}  x, {_, q[_, {}], x_}  x, {_, x_, q[0, _]}  x, {_, _, q[n_, {}]}  q[n - 1, {}], {_, _, q[n_, {x___, _}]}  q[n - 1, {x}], {q[_, {}], _, _}  w, {q[0, {__, x_}], p[y_, _], _}  p[x, y], {q[0, {__, x_}], y_, _}  p[x, y], {p[_, x_], p[y_, _], _}  p[x, y], {p[_, x_], u, _}  x, {p[_, x_], y_, _}  p[x, y], {_, p[x_, _], _}  x, {w, u, _}  u, {w, x_, _}  w, {_, w, x_}  x, {_, r[rn_, x_], _}  x, {_, u, r[_, _]}  u, {_, x_, r[rn_, _]}  r[rn, x], {_, x_, _}  x}]

The initial condition is obtained by applying the rule s[x_, y__]  {r[1, x], y} and then padding with u's.