# Elementary slopes of plane-wide breakout

## TL;DR

This paper models a breakout game using a mathematical framework, identifying conditions for periodic orbits based on the initial slope of the ball, and introduces elementary blocks to describe these orbits.

## Contribution

It provides a novel mathematical description of periodic orbits in a breakout game using elementary blocks and slope conditions.

## Key findings

- Characterization of slopes producing periodic orbits
- Introduction of elementary blocks for orbit description
- Necessary and sufficient conditions for orbit periodicity

## 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.

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Source: https://tomesphere.com/paper/1904.01878