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A272510
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 489", based on the 5-celled von Neumann neighborhood.
4
1, 4, 13, 32, 33, 100, 65, 160, 97, 300, 145, 376, 177, 580, 257, 712, 345, 988, 433, 1112, 465, 1460, 601, 1688, 745, 2100, 897, 2312, 897, 2772, 1081, 3048, 1281, 3612, 1481, 3920, 1505, 4500, 1817, 4848, 1993, 5580, 2209, 5992, 2401, 6628, 2497, 7072
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=489; 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: A218958 A226839 A270976 * A036487 A184632 A212747
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 01 2016
STATUS
approved