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 re(2): Revision by brianjn)

"L must be at least 4 to allow for sequences of moves to return to the starting point wherever possible, any higher value merely retraces pathes already laid."

That statement is not true for values of v that are multiples of 4, where the paths are not retraced, but the mouse ultimately goes off on a diagonal of spirals, rather than on a closed circuit of spirals.

Posted by Charlie on 2008-01-27 11:00:04