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A273642
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 814", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 21, 29, 41, 53, 89, 117, 129, 141, 177, 205, 233, 253, 353, 421, 417, 397, 417, 413, 433, 461, 553, 613, 641, 653, 753, 813, 889, 941, 1265, 1589, 1505, 1317, 1329, 1293, 1265, 1309, 1393, 1373, 1417, 1453, 1513, 1557, 1657, 1693, 1993, 2277, 2233
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=814; 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: A147407 A186297 A272986 * A169649 A273739 A169709
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved