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A272161
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 595", based on the 5-celled von Neumann neighborhood.
5
1, 5, 13, 33, 49, 93, 97, 169, 185, 261, 281, 397, 381, 585, 549, 765, 713, 941, 913, 1149, 1073, 1477, 1409, 1725, 1785, 1885, 1953, 2353, 2261, 2681, 2577, 3073, 3001, 3365, 3393, 3813, 3709, 4313, 4269, 4793, 4761, 5153, 5185, 5821, 5561, 6341, 6249, 6741
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=595; 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: A231799 A146924 A342032 * A272828 A370754 A308812
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 16 2016
STATUS
approved