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

%I A102127 #35 Apr 05 2024 13:06:49
%S A102127 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 A102127 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 A102127 12,4,4,4,4,4,16,4,40,4,4,4,4,4,16,4,4,4,16,4
%N A102127 Interval between successive arrivals at the origin of an LQTL CA.
%C A102127 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 A102127 Andrey Zabolotskiy, <a href="/A102127/b102127.txt">Table of n, a(n) for n = 0..999</a>
%H A102127 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 A102127 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 A102127 (Python)
%o A102127 x = y = direction = 0
%o A102127 cells, a = {}, []
%o A102127 for n in range(1, 1000):
%o A102127     c = cells.get((x, y), 0)
%o A102127     cells[(x, y)] = (c + 1) % 4
%o A102127     direction += [1, 1, -1, -1][c]
%o A102127     (dx, dy) = [(1, 0), (0, 1), (-1, 0), (0, -1)][direction%4]
%o A102127     x += dx;  y += dy
%o A102127     if (x, y) == (0, 0):
%o A102127         a.append(n)
%o A102127 print(a) # A102110
%o A102127 print([x-y for x, y in zip(a, [0]+a)]) # this sequence -  _Andrey Zabolotskiy_, Jan 06 2023
%Y A102127 Cf. A094266, A094867, A099423, A274369, A102369.
%Y A102127 First differences of A102110.
%K A102127 nonn
%O A102127 0,1
%A A102127 _Robert H Barbour_, Feb 14 2005
%E A102127 Terms a(26) and beyond from _Andrey Zabolotskiy_, Jan 06 2023