login
A272416
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 469", based on the 5-celled von Neumann neighborhood.
4
1, 8, 5, 44, 9, 112, 21, 204, 25, 336, 37, 492, 49, 680, 85, 876, 89, 1136, 101, 1420, 113, 1736, 149, 2060, 161, 2440, 197, 2828, 233, 3248, 341, 3628, 345, 4144, 357, 4684, 369, 5256, 405, 5836, 417, 6472, 453, 7116, 489, 7792, 597, 8428, 609, 9192, 645
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=469; 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: A272049 A272350 A271812 * A272153 A272564 A271689
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 29 2016
STATUS
approved