

A287740


Decimal representation of the diagonal from the corner to the origin of the nth stage of growth of the twodimensional cellular automaton defined by "Rule 339", based on the 5celled von Neumann neighborhood.


4



1, 3, 1, 14, 1, 62, 3, 252, 3, 1020, 3, 4092, 3, 16380, 15, 65520, 15, 262128, 15, 1048560, 15, 4194288, 15, 16777200, 15, 67108848, 15, 268435440, 15, 1073741808, 255, 4294967040, 255, 17179868928, 255, 68719476480, 255, 274877906688, 255, 1099511627552
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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 = 339; 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]], 10], {i, 1, stages  1}]


CROSSREFS

Cf. A287738, A287739, A287741.
Sequence in context: A262593 A010290 A074960 * A287751 A287492 A163545
Adjacent sequences: A287737 A287738 A287739 * A287741 A287742 A287743


KEYWORD

nonn,easy


AUTHOR

Robert Price, May 30 2017


STATUS

approved



