A272837 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 545", based on the 5-celled von Neumann neighborhood.

3, 13, 11, 29, 27, 33, 23, 65, 59, 53, 83, 65, 47, 69, 71, 97, 179, 45, 231, 109, 75, 157, 127, 145, 227, 49, 227, 121, 43, 125, 115, 245, 415, 45, 403, 177, 263, 205, 363, 253, 251, 253, 331, 217, 231, 221, 219, 433, 515, 45, 475, 365, 251, 193, 387, 373

Offset

0,1

Comments

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

The first negative term is a(60) = -101. - 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=545; 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. A272834.

Sequence in context: A085416 A107802 A142351 * A273576 A272849 A273613

Adjacent sequences: A272834 A272835 A272836 * A272838 A272839 A272840

Keyword

sign,easy

Author

Robert Price, May 07 2016

Status

approved