

A274993


Decimal representation of the xaxis, from the origin to the right edge, of the nth stage of growth of the twodimensional cellular automaton defined by "Rule 126", based on the 5celled von Neumann neighborhood.


4



1, 3, 3, 3, 11, 19, 59, 3, 11, 51, 187, 771, 2827, 4915, 15291, 3, 11, 51, 187, 771, 2827, 13107, 48059, 196611, 720907, 3342387, 12255419, 50529027, 185273099, 322122547, 1002159035, 3, 11, 51, 187, 771, 2827, 13107, 48059, 196611, 720907, 3342387, 12255419
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OFFSET

0,2


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..126
Robert Price, Diagrams of first 20 stages
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
Wolfram Research, Wolfram Atlas of Simple Programs
Index entries for sequences related to cellular automata
Index to 2D 5Neighbor 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 = 126; 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}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i  1]], 2], {i , 1, stages  1}]


CROSSREFS

Cf. A272609, A273979, A274059.
Sequence in context: A129227 A252748 A097161 * A233202 A101480 A156715
Adjacent sequences: A274990 A274991 A274992 * A274994 A274995 A274996


KEYWORD

nonn,easy


AUTHOR

Robert Price, Dec 03 2016


STATUS

approved



