A271167 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 307", based on the 5-celled von Neumann neighborhood.

4, 4, 23, -19, 91, -79, 167, -143, 267, -275, 399, -331, 515, -555, 787, -675, 891, -887, 1155, -1131, 1412, -1373, 1693, -1605, 1981, -2029, 2313, -2161, 2665, -2732, 3128, -2933, 3313, -3213, 3653, -3632, 4115, -4099, 4771, -4523, 4991, -5115, 5759, -5623

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=307; 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. A271164.

Sequence in context: A268194 A271408 A271249 * A271155 A271132 A270456

Adjacent sequences: A271164 A271165 A271166 * A271168 A271169 A271170

Keyword

sign,easy

Author

Robert Price, Mar 31 2016

Status

approved