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A270733
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 206", based on the 5-celled von Neumann neighborhood.
4
1, 5, 8, 20, 20, 32, 48, 64, 72, 92, 92, 116, 148, 156, 212, 260, 272, 296, 272, 296, 340, 396, 416, 436, 504, 524, 580, 668, 704, 800, 972, 1092, 1080, 1032, 1104, 1160, 1176, 1240, 1280, 1288, 1452, 1572, 1624, 1624, 1680, 1856, 2016, 2140, 2224, 2340
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=206; 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: A194266 A169703 A270091 * A270168 A270984 A270321
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 22 2016
STATUS
approved