A programmable robotic mouse is placed at an intersection on a square grid, the borders of which are extendable as needed.

From its initial location the mouse moves one cell forward. It turns right with its next move incrementing by 1. This incremental process continues up to a certain constraint whereby the mouse resumes the process with a move of one space until that constraint is met again; continue this process until you either return to your starting position or you evidently will never return. What generalisations can be made about how variations of the value of the constraint affect the path forced upon the mouse?

M

Note:It will be necessary to test a range of constraining values.

(In reply to No Subject by nikki)

I am a little amused.  I suggested that I have a "programmable robotic mouse...".  Is there something cultural as to why the feminine gender has been applied to something which in English would be observed by a neutral pronoun (it/its)? Or maybe Nikki refers to her mouse as "she" like we might consider a ship as "she".  Intriguing.

Nikki, I don't understand your issue in suggesting that there is something indefinite about the value of the constraint.  Having started the process, as in the diagram, and as you did in the first parts of your dissertation, you incremented each stage according to: and you continued to a preset number of your choosing ("It turns right with its next move incrementing by 1." 
and you continued to a preset number of your choosing
"until that constraint is met again"). 
Does that not say the constraint is constant for that chosen scenario?

I'm not sure how you might consider redefining the constraint using some of your latter definitions, but they could be interesting.  What both you and Charlie have proposed go very close to what I have in mind.  There is just something additional which might be mentioned, and I'm not sure if Charlie would be able to elucidate that with what he has programmed.

Posted by brianjn on 2008-01-20 09:35:19