Implementation [of TM cellular automaton]

Given a non-deterministic Turing machine with rules in the form above, the rules for a cellular automaton which emulates it can be obtained from

NDTMToCA[tm_] := Flatten[{{_, h, _}  h, {s, _c, _}  e, {s, _, _}  s, {_, s, c[i_]}  s[i], {_, s, x_}  x, {a[_, _], _s, _}  s, {_, a[x_, y_], s[i_]}  a[x, y, i], {x_, _s, _}  x, {_, _, s[i_]}  s[i], Map[Table[With[{b = (#〚Min[Length[#], z]〛 &)[{x, #} /. tm]}, If[Last[b]  -1, {{a[_], a[x, #, z], e}  h, {a[_], a[x, #, z], s}  a[x, #, z], {a[_], a[x, #, z], _}  a[b〚2〛], {a[x, #, z], a[w_], _}  a[b〚1〛, w], {_, a[w_], a[x, #, z]}  a[w]}, {{a[_], a[x, #, z], _}  a[b〚2〛], {a[x, #, z], a[w_], _}  a[w], {_, a[w_], a[x, #, z]}  a[b〚1〛, w]}]], {x, Max[Map[#〚1, 1〛 &, tm]]}, {z, Max[Map[Length[#〚2〛] &, tm]]}] &, Union[Map[#〚1, 2〛 &, tm]]], {_, x_, _}  x}]