Applying iterated mapping to the no-three-in-a-line problem

Abstract

Iterated mapping has seen a lot of success lately in many problems such as bit retrieval, diffraction signal reconstruction, and graph coloring. We add another application of iterated mapping, namely finding solutions to the no-three-in-a-line problem. Given an $n\times n$ grid, we utilize iterated mapping to find $2n$ points such that any straight line (of any slope) drawn will not intersect three of the selected points.