

A290624


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


4



1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 11, 11, 43, 43, 43, 43, 59, 59, 59, 447, 1471, 1471, 1471, 1535, 7679, 7679, 7679, 7679, 65023, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 131071, 524287, 524287, 2097151, 2097151, 2097151, 2097151
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OFFSET

0,9


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 = 870; 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. A290622, A290623, A290625.
Sequence in context: A290546 A291720 A290832 * A290238 A286833 A216852
Adjacent sequences: A290621 A290622 A290623 * A290625 A290626 A290627


KEYWORD

nonn,easy


AUTHOR

Robert Price, Aug 07 2017


STATUS

approved



