Say I have a $10\times10$ plane and I am given two points on the plane, suppose $(0,0)$ and $(10,10)$. What formula or algorithm could be used to trace all the possible paths between these two points? I would like to apply it to a plane of variable area and to any two points within that plane.
Here is a photo that will hopefully clarify
If the algorithm were to draw the route's lines they should be something like this. You could see that there are many other possible routes with an increase in 'turns' but these 4 'main'routes are the ones that span the whole plane to your target