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A270210
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 123", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 41, 12, 109, 16, 209, 20, 337, 28, 501, 28, 689, 52, 913, 60, 1161, 68, 1457, 56, 1757, 120, 2085, 168, 2429, 216, 2841, 224, 3249, 312, 3697, 324, 4193, 332, 4753, 296, 5277, 436, 5821, 564, 6361, 668, 6997, 712, 7613, 852, 8257, 932, 8945, 972
OFFSET
0,2
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=123; 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}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
CROSSREFS
Sequence in context: A270156 A270164 A270181 * A271117 A271297 A178693
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 13 2016
STATUS
approved