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A273430
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 825", based on the 5-celled von Neumann neighborhood.
4
1, 4, 17, 28, 61, 93, 141, 157, 221, 296, 393, 405, 480, 577, 693, 733, 857, 1025, 1145, 1297, 1397, 1597, 1637, 1765, 1965, 2145, 2229, 2433, 2689, 2681, 2981, 3081, 3389, 3537, 3985, 4381, 4413, 4781, 4969, 5105, 5421, 5693, 6073, 6165, 6525, 6725, 7101
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=825; 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: A272769 A273646 A272991 * A273073 A272330 A163736
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved