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A271065
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 262", based on the 5-celled von Neumann neighborhood.
4
1, 5, 4, 20, 9, 33, 13, 65, 20, 92, 37, 101, 45, 133, 69, 197, 85, 213, 89, 233, 93, 309, 97, 393, 113, 473, 133, 517, 105, 429, 184, 784, 220, 740, 252, 796, 264, 824, 264, 1024, 344, 1040, 340, 1068, 332, 1060, 436, 1548, 480, 1496, 592, 1712, 476, 1404
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=262; 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: A307675 A266707 A269695 * A271598 A271133 A272085
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 29 2016
STATUS
approved