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A272085
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 422", based on the 5-celled von Neumann neighborhood.
4
1, 5, 4, 20, 9, 33, 17, 73, 25, 73, 41, 113, 49, 145, 73, 265, 105, 225, 105, 241, 161, 305, 153, 409, 177, 433, 209, 529, 249, 673, 305, 961, 449, 841, 449, 873, 545, 1009, 513, 945, 565, 1029, 641, 1169, 633, 1249, 749, 1701, 793, 1537, 933, 1853, 989
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=422; 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: A271065 A271598 A271133 * A271259 A271409 A246326
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 19 2016
STATUS
approved