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

[Hugo Pfoertner]

>From a comparison of my hand drawing of the terms of A068608 with the
picture http://demonstrations.wolfram.com/AnInfiniteKnightsTour/#snapshot1
provided on the Wolfram demo page
http://demonstrations.wolfram.com/AnInfiniteKnightsTour/ it seems highly
likely that indeed Jay Warendorff's demo was used together with the 8
possible initial steps to create the 8 sequences.

On Sat, May 4, 2019 at 5:31 PM Hugo Pfoertner <yae9911 at gmail.com> wrote:

> A method to construct a tour is Warnsdorff's heuristic together with a
> tie-break rule. The knight's tour Wikipedia page
> https://en.wikipedia.org/wiki/Knight%27s_tour#Warnsdorff's_rule gives a
> link to an article by Squirrel and Cull
> https://github.com/douglassquirrel/warnsdorff/blob/master/5_Squirrel96.pdf?raw=true
> . Their variant of Warnsdorff's method seems to be deterministic and to
> guarantee non-trapping even for very large boards, but I can't see if it is
> the one applied in the 8 sequences.
>
> On Sat, May 4, 2019 at 5:11 PM Hans Havermann <gladhobo at bell.net> wrote:
>
>> > If we don't have an explicit construction for any of the 8 "tours", how
>> can we be sure that they don't get trapped after a while?
>>
>> A spiral constructions does exist. There's a Wolfram Demonstration
>> version by Jay Warendorff that appears to correspond to A068610. I'll see
>> if I can at least verify the existing terms.
>>
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>>
>