[seqfan] Re: Knight's tour on infinite board

[Hans Havermann]

> It is dependant of course on the Ellermann spiral numbering scheme.

Ellermann's "Ulam spiral" variant goes north, then spirals clockwise. Every Ulam spiral I've looked at in a search just now goes east, then spirals counter-clockwise. The knight's tour sequences would of course be different superimposed on a "proper" Ulam spiral.

> The tour starts by filling in a central 5-by-5 square, starting in the square's center and ending in its SE corner. It then jumps 2 south and 1 east and proceeds to circle the 5-by-5 square clockwise four times filling in the now-9-by-9 square and ending in its SE corner. And so on.

If we flip the two-dimensional knight's tour over (in three-space) the spiral tour now runs counter-clockwise. Superimposed on Ellermann's Ulam spiral variant would generate new sequences differing from the eight that we have. So there is nothing really special about these eight sequences.