The Convergence of Difference Boxes
Antonio Behn, Christopher M. Kribs, Vadim Ponomarenko · American Mathematical Monthly · 2005
We consider an elementary mathematical puzzle known as a "difference box" in terms of a discrete map from R4 to R4 or, canonically, from a subset of the first quadrant of R2 into itself. We find the map's unique canonical fixed point and answer the general question of how many iterations a given "difference box" takes to reach zero.