These are the trajectories that about half of people prefer, over all other possibilities.
You can see such preferences occur live in this video (chosen to start at 35:30, where it happens).
Read about how this family arises, in section 4.2, starting on page 24, of this paper.
The label e.g. '12' means that this is the short trajectory at location '12' in the tree of periodic directions (see section 2.2 and Figure 7 of the paper).
12
102
1002
10002
100002
1000002
10000002
100000002
1000000002
10000000002
100000000002
1000000000002
10000000000002
100000000000002
1000000000000002
10000000000000002
100000000000000002
1000000000000000002
10000000000000000002
100000000000000000002