A273211 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 609", based on the 5-celled von Neumann neighborhood.

3, 17, 8, 43, 12, 57, 27, 80, 41, 51, 37, 100, 48, 72, 32, 179, 100, 173, 72, 80, 123, 113, 28, 195, 181, 143, 133, 175, 197, 155, -35, 311, 268, 284, 100, 296, 120, 156, 144, 244, 332, 176, 172, 316, 372, 109, 15, 493, 523, 148, 97, 407, 420, 176, 348, 276

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

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=609; 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. A273208.

Sequence in context: A124689 A367877 A093844 * A273273 A273249 A273303

Adjacent sequences: A273208 A273209 A273210 * A273212 A273213 A273214

Keyword

sign,easy

Author

Robert Price, May 17 2016

Status

approved