n=6: 77 directions of short trajectories of length <= 12.0; 9 sample points on a side per direction
parity of the type (n even) | ratios of the preclosed lengths | reduced factors per length | number of directions | example (reachable point, unreduced factors)
   0 | (1.0,) | ((1,),) | 51 | ((1, 0), ((3,),))
   1 | (1.0, 2.0) | ((1,), (1,)) | 8 | ((8, 5), ((1,), (1,)))
   1 | (1.0, 2.0) | ((3,), (1,)) | 18 | ((-1, 2), ((3,), (1,)))
patterns with a reduced factor equal to n: 0
