

A288302


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 438", based on the 5celled von Neumann neighborhood.


4



1, 1, 2, 2, 6, 6, 14, 14, 29, 22, 54, 58, 118, 78, 222, 226, 478, 318, 838, 934, 2014, 1442, 3538, 3694, 7594, 6106, 14118, 15322, 30502, 24410, 55294, 63422, 72191, 130828, 194364, 262143, 278296, 518104, 780284, 1022946, 1271782, 1808794, 3139518, 3676662
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OFFSET

0,3


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 = 438; 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. A288300, A288301, A288303.
Sequence in context: A228315 A120690 A165124 * A286409 A285610 A056453
Adjacent sequences: A288299 A288300 A288301 * A288303 A288304 A288305


KEYWORD

nonn,easy


AUTHOR

Robert Price, Jun 07 2017


STATUS

approved



