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A271016
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 251", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 41, 21, 101, 49, 185, 61, 309, 97, 449, 133, 613, 225, 761, 237, 1013, 273, 1281, 309, 1573, 417, 1841, 453, 2197, 561, 2537, 669, 2885, 961, 3065, 973, 3573, 1009, 4097, 1045, 4645, 1153, 5169, 1189, 5781, 1297, 6377, 1405, 6981, 1729, 7409, 1765
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=251; 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: A270622 A270673 A269702 * A176967 A110421 A176751
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 28 2016
STATUS
approved