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

Wed May 8 07:09:14 CEST 2019

yae9911 at gmail.com (Hugo Pfoertner) writes:
>
> A306659 and A306660

Are you sure about first step to x=2, y=1 ?  It has inner-most ring
slightly different than some code I wrote in the past and which I
believe matches A068608.  (Math::PlanePath::KnightSpiral)

  http://user42.tuxfamily.org/temporary/knight-spiral-lines.png

This makes A068608 from square spiral coordinates X=A174344, Y=A274923.
(Incidentally, maybe could tweak the name of A174344 to just "square
spiral" like A274923 has.)

Stepping to the outer ring is 2 moves of same direction.  I thought it
attractive that the very first step is parallel to the later outward
steps.  In your code it might be as simple as initial p+=move[2,].
But whatever works, is right, etc, of course.

I don't remember any particular reason I have each step-to-next-ring
occurring at the south-east corners.  Maybe it was to traverse the east
side first.  Others have done the pattern yet other ways around.
Eg. (as noted arriving at A068614, perhaps ...)

http://web.archive.org/web/1id_/http://www.borderschess.org/Infinite.gif
http://web.archive.org/web/20161028114643id_/http://www.borderschess.org/KTart.htm

(Possible dodginess in the html colours might make the text invisible.
Try text mode like w3m, or delete the colours in the <BODY ...>)