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A273115
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 590", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 17, 17, 37, 49, 41, 57, 77, 97, 113, 141, 149, 225, 189, 249, 249, 361, 257, 349, 409, 437, 529, 525, 537, 637, 681, 685, 833, 853, 977, 1073, 957, 1133, 1077, 1133, 1253, 1193, 1393, 1405, 1469, 1537, 1721, 1793, 1953, 1949, 2205, 1985, 2225, 2365
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=590; 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: A362108 A272742 A273534 * A273687 A102179 A345920
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 15 2016
STATUS
approved