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A284358 Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 902", based on the 5-celled von Neumann neighborhood. 6
1, 3, 5, 11, 21, 43, 69, 219, 261, 795, 1301, 2603, 5205, 10475, 20613, 41883, 85701, 190555, 334037, 741995, 1553813, 2398379, 8317125, 9799771, 33206405, 36491675, 116555925, 168394923, 505316309, 878281067, 1561233029, 3341360027, 7983546565, 9842622555 (list; graph; refs; listen; history; text; internal format)
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 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 = 902; 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. A284355, A284356, A284357.

Sequence in context: A122997 A146042 A291219 * A283584 A283702 A284539

Adjacent sequences:  A284355 A284356 A284357 * A284359 A284360 A284361

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 25 2017

STATUS

approved

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Last modified October 29 04:54 EDT 2020. Contains 338066 sequences. (Running on oeis4.)