login
A273212
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 611", based on the 5-celled von Neumann neighborhood.
4
1, 5, 17, 37, 61, 97, 133, 173, 209, 337, 397, 461, 529, 621, 681, 757, 821, 1117, 1209, 1377, 1469, 1653, 1765, 1865, 1961, 2293, 2401, 2593, 2697, 2897, 3025, 3197, 3277, 3961, 4021, 4481, 4613, 4909, 5209, 5405, 5585, 6021, 6137, 6389, 6669, 6989, 7237
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=611; 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: A257582 A339988 A273538 * A273274 A357058 A273250
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 17 2016
STATUS
approved