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3:41 PM
(*start*)
(*When the divisor and the constant c are the same then is the middle \
column sequence nonperiodic?*)
Clear[t, n, k];
nn = 180;
divisor = 2;
c = divisor;
t[1, k_] := t[1, k] = If[k == nn, 1, 0];
t[n_, k_] :=
t[n, k] =
Mod[t[-1 + n, -1 + k] + t[-1 + n, k] +
c* t[-1 + n, -1 + k] t[-1 + n,
k] + (+1 + c* t[-1 + n, -1 + k]) (+1 + t[-1 + n, k]) t[-1 + n,
1 + k], divisor]
Table[t[n, nn], {n, 1, nn}]
ListLinePlot[Table[t[n, nn], {n, 1, nn}]]
ArrayPlot[Table[Table[t[n, k], {k, 1, 2*nn}], {n, 1, nn}]]
 
4:38 PM
(*start*)"Rule 30 is invariant when the constant c is a multiple of \
the divisor d."
"Counts to 12"
Monitor[Table[Clear[t, n, k];
nn = 180;
d = 2;
c = d*m;
t[1, k_] := t[1, k] = If[k == nn, 1, 0];
t[n_, k_] :=
t[n, k] =
Mod[t[-1 + n, -1 + k] + t[-1 + n, k] +
c*t[-1 + n, -1 + k] t[-1 + n,
k] + (+1 + c*t[-1 + n, -1 + k]) (+1 + t[-1 + n, k]) t[-1 + n,
1 + k], d];
ArrayPlot[Table[Table[t[n, k], {k, 1, 2*nn}], {n, 1, nn}]], {m, 1,
12}], m]
(*end*)
 

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