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A287854 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 366", based on the 5-celled von Neumann neighborhood. 4
1, 1, 0, 1, 2, 1, 2, 1, 2, 13, 2, 1, 14, 1, 0, 15, 0, 16, 131, 16, 128, 115, 140, 68, 180, 72, 137, 128, 65, 162, 33, 194, 37, 58, 32779, 12, 33028, 8, 33289, 16640, 34367, 25088, 33792, 25615, 39440, 25600, 39455, 25600, 39424, 25631, 39808, 25628, 33795 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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 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 = 366; 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. A287852, A287853, A287855.

Sequence in context: A106157 A181816 A113738 * A245714 A092953 A058574

Adjacent sequences:  A287851 A287852 A287853 * A287855 A287856 A287857

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jun 01 2017

STATUS

approved

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Last modified December 2 01:13 EST 2021. Contains 349435 sequences. (Running on oeis4.)