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A273687
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 846", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 17, 17, 37, 53, 49, 73, 97, 89, 109, 129, 181, 241, 261, 297, 245, 309, 325, 401, 425, 477, 557, 565, 581, 613, 681, 789, 857, 761, 1081, 981, 1049, 1193, 1097, 1229, 1213, 1305, 1545, 1513, 1569, 1677, 1737, 1837, 1857, 1913, 2121, 2065, 2233, 2353
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=846; 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: A272742 A273534 A273115 * A102179 A345920 A315112
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved