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A282950 Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 531", based on the 5-celled von Neumann neighborhood. 4
1, 1, 1, 1, 101, 101, 10001, 10101, 1011001, 1000001, 100011101, 101001011, 10110001101, 10000100011, 1000110101001, 1010001101001, 101100100011001, 100000001000001, 10001111100011101, 10100100001000001, 1011000101101011101, 1000010010001001001 (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 = 531; 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[1, i]], 10], {i, 1, stages - 1}]

CROSSREFS

Cf. A282951, A282952, A282953.

Sequence in context: A266667 A241495 A282980 * A283087 A283140 A283210

Adjacent sequences:  A282947 A282948 A282949 * A282951 A282952 A282953

KEYWORD

nonn,easy

AUTHOR

Robert Price, Feb 25 2017

STATUS

approved

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Last modified February 19 16:55 EST 2018. Contains 299356 sequences. (Running on oeis4.)