login
A273388
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 662", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 21, 21, 45, 33, 81, 49, 109, 73, 181, 105, 241, 89, 297, 181, 401, 137, 449, 289, 585, 229, 637, 381, 821, 305, 893, 477, 1089, 361, 1201, 569, 1445, 457, 1561, 701, 1825, 549, 1929, 817, 2225, 657, 2357, 965, 2685, 765, 2805, 1097, 3165, 889, 3313
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=662; 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: A323110 A272786 A273150 * A273449 A297362 A376288
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 21 2016
STATUS
approved