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A272252
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 449", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 24, 21, 72, 45, 112, 93, 224, 117, 320, 173, 464, 205, 528, 293, 848, 225, 1100, 145, 1488, 361, 1396, 593, 1744, 561, 2012, 637, 2384, 669, 2336, 1053, 2952, 861, 3600, 589, 4208, 1073, 4140, 1241, 4876, 1145, 5176, 1573, 5556, 1509, 6008, 1621
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=449; 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: A196034 A196037 A270685 * A067801 A062775 A288105
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 23 2016
STATUS
approved