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A272016
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 417", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 28, 17, 68, 41, 140, 33, 260, 101, 340, 61, 536, 169, 620, 65, 1028, 197, 1172, 185, 1280, 365, 1416, 165, 2096, 473, 2144, 309, 2512, 637, 2548, 309, 3544, 729, 3524, 549, 3920, 973, 3940, 645, 4928, 1181, 4928, 845, 5768, 1341, 5812, 965, 6976
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=417; 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: A256096 A071913 A007872 * A272089 A270720 A272280
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 17 2016
STATUS
approved