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A283607 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 670", based on the 5-celled von Neumann neighborhood. 4
1, 3, 7, 15, 23, 63, 119, 255, 375, 1023, 1783, 4095, 6647, 16383, 28663, 65535, 131063, 262143, 524279, 1048575, 2097143, 4194303, 8388599, 16777215, 33554423, 67108863, 134217719, 268435455, 536870903, 1073741823, 2147483639, 4294967295, 8589934583 (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 = 670; 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. A283604, A283605, A283606.

Sequence in context: A284090 A284422 A283865 * A001213 A066044 A066460

Adjacent sequences:  A283604 A283605 A283606 * A283608 A283609 A283610

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 11 2017

STATUS

approved

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Last modified June 22 20:06 EDT 2021. Contains 345388 sequences. (Running on oeis4.)