login
A273792
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 934", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 17, 9, 29, 21, 65, 33, 61, 45, 121, 73, 137, 81, 229, 153, 253, 185, 341, 257, 413, 385, 581, 529, 673, 625, 845, 757, 937, 897, 1217, 1117, 1185, 1169, 1485, 1425, 1625, 1601, 1849, 1817, 2025, 1985, 2325, 2229, 2509, 2493, 2829, 2745, 2961, 3001
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=934; 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: A246333 A079317 A273482 * A273855 A175614 A214022
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 30 2016
STATUS
approved