A102127 - OEIS

%I #35 Apr 05 2024 13:06:49

%S 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,

%T 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,

%U 12,4,4,4,4,4,16,4,40,4,4,4,4,4,16,4,4,4,16,4

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

%C 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

%H Andrey Zabolotskiy, <a href="/A102127/b102127.txt">Table of n, a(n) for n = 0..999</a>

%H Robert H. Barbour, <a href="https://www.complex-systems.com/abstracts/v17_i02_a01/">Two-dimensional Four Color Cellular Automaton: Surface Explorations</a>, Complex Systems, 17 (2007), 103-112.

%H Palash Sarkar, <a href="https://www.cs.ucf.edu/~dcm/Teaching/COT4810-Spring2011/Literature/CellularAutomata.pdf">A Brief History of Cellular Automata</a>, ACM Computing Surveys, Vol. 32, No. 1, March 2000, 80-107.

%o (Python)

%o x = y = direction = 0

%o cells, a = {}, []

%o for n in range(1, 1000):

%o     c = cells.get((x, y), 0)

%o     cells[(x, y)] = (c + 1) % 4

%o     direction += [1, 1, -1, -1][c]

%o     (dx, dy) = [(1, 0), (0, 1), (-1, 0), (0, -1)][direction%4]

%o     x += dx;  y += dy

%o     if (x, y) == (0, 0):

%o         a.append(n)

%o print(a) # A102110

%o print([x-y for x, y in zip(a, [0]+a)]) # this sequence -  _Andrey Zabolotskiy_, Jan 06 2023

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

%Y First differences of A102110.

%K nonn

%O 0,1

%A _Robert H Barbour_, Feb 14 2005

%E Terms a(26) and beyond from _Andrey Zabolotskiy_, Jan 06 2023