A094266 -id:A094266 - cp's OEIS frontend

A099423 Lean quaternary temporal logic [LQTL] cumulative column frequencies of LQTL logic in A094266.

1, 0, 0, 0, 2, 1, 0, 0, 3, 3, 1, 0, 4, 6, 4, 1, 6, 10, 10, 5, 12, 16, 20, 15, 28, 28, 36, 35, 64, 56, 64, 71, 136, 120, 120, 135, 272, 256, 240, 255, 528, 528, 496, 495, 1024, 1056, 1024, 991, 2016, 2080, 2080, 2015, 4032, 4096, 4160, 4095, 8128, 8128, 8256, 8255

Offset: 0

Robert H Barbour, Nov 17 2004; corrected Jun 10 2005

Appears to satisfy the recurrence: a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 4*a(n-16). - Chai Wah Wu, May 25 2016

This is a table read by rows of length 4. Every row is formed from the corresponding row of the table A094266 according to the rule: a, b, c, d -> b, c, d, a-1. - Andrey Zabolotskiy, Jan 06 2023

Robert H. Barbour, Two-dimensional Four Color Cellular Automaton: Surface Explorations, Complex Systems, 17 (2007), 103-112.

Cf. A094266 (first differences row-wise).

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

Original entry on oeis.org

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

A094867 Number of iterations of the LQTL cellular automaton required to generate a square of cells in identical states.

Original entry on oeis.org

4, 8, 32, 64, 416, 832

Offset: 0

Robert H Barbour and J. Chapman, Jun 15 2004

For the definition of the LQTL CA, see A102127. The square of size 1 on iteration 1 is not included.

			After step a(5) = 832 of the cellular automaton, the nonempty cells form a 8x8 square, all cells in state 2.

P. Sarkar, A Brief History of Cellular Automata, ACM Computing Surveys, Vol. 32, No. 1, March 2000.

Cf. A094266, A102110, A204810.

Edited by Andrey Zabolotskiy, Nov 05 2023

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

cp's OEIS Frontend

A099423 Lean quaternary temporal logic [LQTL] cumulative column frequencies of LQTL logic in A094266.

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

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A094867 Number of iterations of the LQTL cellular automaton required to generate a square of cells in identical states.

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

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