A272156 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 437", based on the 5-celled von Neumann neighborhood.

7, -3, 39, -35, 103, -91, 199, -195, 319, -303, 451, -435, 655, -659, 847, -795, 1071, -1099, 1367, -1295, 1631, -1615, 1943, -1915, 2283, -2231, 2639, -2575, 3003, -2951, 3415, -3375, 3887, -3931, 4483, -4423, 4975, -4919, 5511, -5471, 6095, -6047, 6735

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=437; 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. A272153.

Sequence in context: A272294 A272567 A272419 * A271815 A194778 A272010

Adjacent sequences: A272153 A272154 A272155 * A272157 A272158 A272159

Keyword

sign,easy

Author

Robert Price, Apr 21 2016

Status

approved