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A270235
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 133", based on the 5-celled von Neumann neighborhood.
1
7, -4, 36, -23, 83, -75, 159, -128, 261, -269, 381, -309, 529, -577, 761, -705, 945, -905, 1065, -921, 1317, -1517, 1933, -1765, 1880, -1755, 2147, -2159, 2691, -2707, 3019, -2867, 3343, -3335, 3655, -3411, 4091, -4247, 4799, -4707, 5187, -5043, 5575, -5523
OFFSET
0,1
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=133; stages=128;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
CROSSREFS
Cf. A270232.
Sequence in context: A282798 A282802 A248278 * A270719 A270460 A270949
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 13 2016
STATUS
approved