login
A272750
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 531", based on the 5-celled von Neumann neighborhood.
4
1, 5, 13, 29, 49, 89, 97, 165, 177, 273, 277, 385, 389, 545, 549, 701, 697, 889, 917, 1057, 1097, 1301, 1409, 1557, 1681, 1925, 1821, 2213, 2173, 2465, 2601, 2821, 2853, 3193, 3253, 3541, 3481, 3989, 4057, 4437, 4493, 4853, 4797, 5557, 5381, 5933, 5749, 6589
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=531; 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: A230281 A093836 A000328 * A272801 A100438 A129371
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 05 2016
STATUS
approved