n=8: 35 directions of short trajectories of length <= 8.0; 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, 1.414214) | ((2,), (1,)) | 22 | ((1, 0, 0, 0), ((2,), (1,)))
   1 | (1.0, 2.414214) | ((1,), (1,)) | 13 | ((0, 0, 1, 1), ((4,), (4,)))
patterns with a reduced factor equal to n: 0
