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A102127
Interval between successive arrivals at the origin of an LQTL CA.
6
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
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
First differences of A102110.
Sequence in context: A179526 A098525 A141666 * A201625 A223824 A218056
KEYWORD
nonn
AUTHOR
Robert H Barbour, Feb 14 2005
EXTENSIONS
Terms a(26) and beyond from Andrey Zabolotskiy, Jan 06 2023
STATUS
approved