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): No Subject by nikki)

Here's an example of a path using a different constraint: if the distance from the original spot is over 20 units, revert to step size 1. It's pretty useless, as it gets stuck, in this case, on the lower right corner in a square of side 1:

 

   r                           s

     n                       o

       j                   k

         f               g

           b           c

             7       8

               3   4

                 0
               2 1

             6     5

           a         9

         e             d

       i                 h

     m                     l

   q                         pv zwA
                                yxB
                              ut

where the B is then followed by xwABxwAB... interminably. Pretty useless, but an example of a different rule from a fixed maximum step size as a basis or constraint.

Posted by Charlie on 2008-01-21 01:49:47