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

0,1

Comments

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

Links

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.

Prog

(Python)
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

Crossrefs

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

First differences of A102110.

Sequence in context: A179526 A098525 A141666 * A201625 A223824 A218056

Adjacent sequences: A102124 A102125 A102126 * A102128 A102129 A102130

Keyword

nonn

Author

Robert H Barbour, Feb 14 2005

Extensions

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

Status

approved