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A272194
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 446", based on the 5-celled von Neumann neighborhood.
4
1, 5, 12, 25, 28, 52, 64, 109, 76, 141, 152, 233, 192, 281, 312, 393, 284, 445, 456, 625, 504, 689, 720, 869, 684, 981, 912, 1169, 1084, 1213, 1380, 1469, 1260, 1633, 1636, 1973, 1724, 2061, 2116, 2409, 2008, 2585, 2420, 2813, 2656, 2897, 3232, 3197, 2960
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=446; 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: A108314 A337065 A079425 * A169699 A109624 A081501
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 23 2016
STATUS
approved