n=15: 10 directions of short trajectories of length <= 4.0; 7 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, 1.956295, 2.827091, 3.574329, 4.165352, 4.574329, 4.783386) | ((5,), (5,), (5,), (5,), (1,), (5,), (5,)) | 2 | ((2, 0, 1, 0, 0, 0, 0, 0), ((5,), (5,), (5,), (5,), (1,), (5,), (5,)))
   0 | (1.0, 1.956295, 2.827091, 3.574329, 4.165352, 4.574329, 4.783386) | ((15,), (15,), (5,), (15,), (3,), (5,), (15,)) | 8 | ((1, 0, 0, 0, 0, 0, 0, 0), ((15,), (15,), (5,), (15,), (3,), (5,), (15,)))
patterns with a reduced factor equal to n: 1
