Twist, twist, twist, turn , twist, twist, twist, turn , twist, twist, twist, turn

produces:


0, 1, 2, 3, - 1
3
 , 2
3
 , 5
3
 , 8
3
 , - 3
8
 , 5
8
 , 13
8
 , 21
8
 , - 8
21



To return to zero:

if the fraction is negative, then twist (+1);
if the fraction is positive, then turn (-1/x).

twist, turn , twist, twist, turn , twist, twist, twist, turn , twist, twist, twist, turn , twist, twist:
13/21, -21/13, -8/13, 5/13, -13/5, -8/5, -3/5, 2/5, -5/2, -3/2, -1/2, 1/2, -2, -1, 0