Elementary slopes of plane-wide breakout

Abstract

We consider a mathematical model of the breakout game where $\mathbb{R}^2$ is covered by unit square bricks everywhere except in one place. We introduce elementary blocks (particular sets of bricks) in order to describe a family of periodic (in a breakout-appropriate sense) orbits. Necessary and sufficient conditions for slopes (the initial direction of the ball) to produce these orbits are given.