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A273069
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 581", based on the 5-celled von Neumann neighborhood.
4
1, 8, 20, 41, 57, 96, 116, 189, 197, 273, 272, 457, 457, 581, 549, 805, 708, 929, 921, 1161, 1173, 1353, 1317, 1780, 1649, 1857, 1937, 2324, 2105, 2592, 2569, 3000, 2860, 3333, 3073, 3772, 3756, 3945, 4105, 4549, 4628, 4909, 5048, 5381, 5708, 5769, 6080
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=581; 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: A086062 A006416 A375717 * A273144 A272842 A272924
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 14 2016
STATUS
approved