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

Author

Robert H Barbour, Feb 14 2005

Keywords

• nonn

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.

Crossrefs

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

First differences of A102110.

Programs

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

Extensions

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