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

[Hans Havermann]

HH: "... we have at each expansion point a binary choice of whether to go clockwise or counterclockwise. This would suggest an infinite number of possible knight's tours on an infinite chessboard."

I've illustrated the traditional infinite knight's tour example with a variant that alternates clockwise and counterclockwise modes of knight travel around the center. It's on the left, here:

http://chesswanks.com/pot/InfiniteKnightTours.jpg

On the right, I have drawn a radically different infinite knight's tour. It shouldn't take too long to figure it out. This makes my quoted assertion by Joel David Hamkins ("you can assemble the 5×5 blocks in any tiling, as long as each block is attached by a side to the next") a little more tangible.