A270569 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 323", based on the 5-celled von Neumann neighborhood.

1, 5, 5, 36, 9, 96, 17, 188, 21, 312, 25, 468, 29, 656, 33, 876, 37, 1128, 41, 1412, 45, 1728, 49, 2076, 53, 2456, 57, 2868, 61, 3312, 65, 3788, 69, 4296, 73, 4836, 77, 5408, 81, 6012, 85, 6648, 89, 7316, 93, 8016, 97, 8748, 101, 9512, 105, 10308, 109, 11136

Offset

0,2

Comments

Initialized with a single black (ON) cell at stage zero.

Similar to A269782.

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

Robert Price, Table of n, a(n) for n = 0..128

Robert Price, Diagrams of the first 20 stages.

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

Mathematica

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=323; 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

Cf. A269782.

Sequence in context: A374508 A375993 A271054 * A270290 A270897 A270325

Adjacent sequences: A270566 A270567 A270568 * A270570 A270571 A270572

Keyword

nonn,easy

Author

Robert Price, Apr 02 2016

Status

approved