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.

Replaced symbolic periodicity by relative periodicity. Reworked introduction. 18 pages, 7 figures