A273215 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 611", based on the 5-celled von Neumann neighborhood.

4, 12, 20, 24, 36, 36, 40, 36, 128, 60, 64, 68, 92, 60, 76, 64, 296, 92, 168, 92, 184, 112, 100, 96, 332, 108, 192, 104, 200, 128, 172, 80, 684, 60, 460, 132, 296, 300, 196, 180, 436, 116, 252, 280, 320, 248, 112, 224, 780, 204, 380, 336, 380, 244, 368, 16

Offset

0,1

Comments

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

The first negative term is a(65) = -28. - Georg Fischer, Feb 15 2019

References

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

Links

Robert Price, Table of n, a(n) for n = 0..127

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=611; 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}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)

Crossrefs

Cf. A273212.

Sequence in context: A050426 A061820 A273541 * A273277 A100717 A365883

Adjacent sequences: A273212 A273213 A273214 * A273216 A273217 A273218

Keyword

sign,easy

Author

Robert Price, May 17 2016

Status

approved