A273491 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 758", based on the 5-celled von Neumann neighborhood.

4, 4, 12, 12, 12, 16, 24, 44, 28, 32, 32, 60, 28, 48, 56, 76, 60, 64, 64, 92, 60, 80, 80, 108, 76, 96, 80, 124, 60, 112, 120, 140, 124, 128, 128, 156, 124, 144, 144, 172, 140, 160, 144, 188, 124, 176, 176, 204, 172, 192, 176, 220, 156, 208, 192, 236, 172

Offset

0,1

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

Table of n, a(n) for n=0..56.

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=758; 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. A273486.

Sequence in context: A241496 A273412 A206488 * A168398 A281913 A178776

Adjacent sequences: A273488 A273489 A273490 * A273492 A273493 A273494

Keyword

nonn,easy

Author

Robert Price, May 23 2016

Status

approved