A094867 -id:A094867 - cp's OEIS frontend

A102127 Interval between successive arrivals at the origin of an LQTL CA.

4, 4, 4, 16, 4, 4, 4, 16, 4, 4, 4, 4, 4, 40, 4, 16, 4, 4, 4, 4, 12, 4, 4, 8, 4, 40, 4, 4, 4, 4, 4, 88, 4, 40, 4, 4, 4, 4, 4, 16, 4, 4, 4, 16, 4, 4, 4, 4, 4, 40, 4, 88, 4, 4, 4, 4, 4, 40, 4, 8, 4, 12, 4, 4, 4, 4, 4, 16, 4, 40, 4, 4, 4, 4, 4, 16, 4, 4, 4, 16, 4

Offset: 0

Robert H Barbour, Feb 14 2005

nonn

The "LQTL CA" is similar to the Langton's ant but has 4 states. The ant turns right from the cells with states 0, 1 and left from the cells with states 2, 3 and changes the state of the cell according to the rules 0 -> 1 -> 2 -> 3 -> 0. - Andrey Zabolotskiy, Jan 06 2023

Andrey Zabolotskiy, Table of n, a(n) for n = 0..999
Robert H. Barbour, Two-dimensional Four Color Cellular Automaton: Surface Explorations, Complex Systems, 17 (2007), 103-112.
Palash Sarkar, A Brief History of Cellular Automata, ACM Computing Surveys, Vol. 32, No. 1, March 2000, 80-107.

Cf. A094266, A094867, A099423, A274369, A102369.

First differences of A102110.

x = y = direction = 0
cells, a = {}, []
for n in range(1, 1000):
    c = cells.get((x, y), 0)
    cells[(x, y)] = (c + 1) % 4
    direction += [1, 1, -1, -1][c]
    (dx, dy) = [(1, 0), (0, 1), (-1, 0), (0, -1)][direction%4]
    x += dx;  y += dy
    if (x, y) == (0, 0):
        a.append(n)
print(a) # A102110
print([x-y for x, y in zip(a, [0]+a)]) # this sequence -  Andrey Zabolotskiy, Jan 06 2023

Terms a(26) and beyond from Andrey Zabolotskiy, Jan 06 2023

A126980 a(n) = 14*n + 47.

Original entry on oeis.org

47, 61, 75, 89, 103, 117, 131, 145, 159, 173, 187, 201, 215, 229, 243, 257, 271, 285, 299, 313, 327, 341, 355, 369, 383, 397, 411, 425, 439, 453, 467, 481, 495, 509, 523, 537, 551, 565, 579, 593, 607, 621, 635, 649, 663, 677, 691, 705, 719, 733, 747

Offset: 0

Robert H Barbour, Mar 20 2007, Jun 12 2007

Superhighway created by 'LQTL Ant' L90R135L90R135 from iteration 47 where the Ant moves in a 'Moore neighborhood' (nine cells), the L indicates a left turn, the R a right turn, and the numerical value is the turn angle (in degrees) at each iteration.

P. Sakar, "A Brief History of Cellular Automata," ACM Computing Surveys, vol. 32, 2000.
S. Wolfram, A New Kind of Science, 1st ed. Il.: Wolfram Media Inc., 2002.

Diana Mecum, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A017041, A019430, A094867, A126978, A126979.

[14*n + 47: n in [0..60] ]; // Vincenzo Librandi, Jul 18 2011

Table[14*n + 47, {n, 0, 60}] (* Stefan Steinerberger, Jun 17 2007 *)
LinearRecurrence[{2,-1}, {47,61}, 50] (* G. C. Greubel, May 30 2016 *)

From Chai Wah Wu, May 30 2016: (Start)
a(n) = 2*a(n-1) - a(n-2) for n > 1.
G.f.: (-33*x + 47)/(x - 1)^2. (End)
E.g.f.: (47 + 14*x)*exp(x). - G. C. Greubel, May 30 2016

More terms from Stefan Steinerberger and Diana L. Mecum, Jun 17 2007

A102110 Iterations during which LQTL cellular automaton passes through the origin.

Original entry on oeis.org

4, 8, 12, 28, 32, 36, 40, 56, 60, 64, 68, 72, 76, 116, 120, 136, 140, 144, 148, 152, 164, 168, 172, 180, 184, 224, 228, 232, 236, 240, 244, 332, 336, 376, 380, 384, 388, 392, 396, 412, 416, 420, 424, 440, 444, 448, 452, 456, 460, 500, 504, 592, 596, 600, 604

Offset: 1

Robert H Barbour, Feb 14 2005

Robert H. Barbour, Two-dimensional Four Color Cellular Automaton: Surface Explorations, Complex Systems, 17 (2007), 103-112.
Palash Sarkar, A Brief History of Cellular Automata, ACM Computing Surveys, Vol. 32 (2000), No. 1 March, p. 80-107.

Cf. A094266, A094867, A099423.

Cumulative sums of A102127.

Terms a(19) and beyond from Andrey Zabolotskiy, Jan 06 2023

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A102127 Interval between successive arrivals at the origin of an LQTL CA.

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A126980 a(n) = 14*n + 47.

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A102110 Iterations during which LQTL cellular automaton passes through the origin.

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