A270720 Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 201", based on the 5-celled von Neumann neighborhood.

1, 4, 9, 28, 17, 80, 28, 133, 64, 241, 72, 348, 109, 532, 137, 656, 212, 865, 204, 1049, 296, 1349, 304, 1557, 432, 1781, 496, 2085, 632, 2421, 720, 2705, 744, 3105, 912, 3504, 849, 4032, 1160, 4349, 1128, 4904, 1233, 5228, 1361, 5848, 1480, 6237, 1660, 6825

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.

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=201; 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: A007872 A272016 A272089 * A272280 A087726 A270891

Adjacent sequences: A270717 A270718 A270719 * A270721 A270722 A270723

Keyword

nonn,easy,changed

Author

Robert Price, Mar 22 2016

Status

approved