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A271117
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 283", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 44, 5, 109, 16, 213, 5, 341, 25, 512, 17, 685, 61, 908, 37, 1177, 53, 1452, 57, 1713, 113, 2056, 113, 2437, 113, 2824, 149, 3244, 189, 3709, 173, 4257, 216, 4737, 244, 5301, 232, 5837, 364, 6397, 356, 7049, 516, 7645, 509, 8357, 480, 9097, 524, 9889
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=283; 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: A270164 A270181 A270210 * A271297 A178693 A065238
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 31 2016
STATUS
approved