A272785 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 533", based on the 5-celled von Neumann neighborhood.

7, 12, 17, 27, 20, 57, 8, 95, 5, 112, 15, 108, 57, 132, 11, 176, 17, 196, 39, 188, 49, 212, 79, 156, 173, 152, 139, 184, 149, 212, 187, 152, 229, 188, 279, 76, 369, 88, 435, 0, 449, 128, 347, 96, 457, 256, 191, 292, 317, 356, 315, 140, 497, 248, 459, 8, 737

Offset

0,1

Comments

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

First negative term is a(59) = -68. - 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=533; 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. A272782.

Sequence in context: A272741 A091573 A183046 * A272808 A092094 A064665

Adjacent sequences: A272782 A272783 A272784 * A272786 A272787 A272788

Keyword

sign,easy

Author

Robert Price, May 06 2016

Status

approved