Billiards with Bombs

Abstract

In this paper, we define a variant of billiards in which the ball bounces around a square grid erasing walls as it goes. We prove that there exist periodic tunnels with arbitrarily large period from any possible starting point, that there exist non-periodic tunnels from any possible starting point, and that there are versions of the problem for which the same starting point and initial direction result in periodic tunnels of arbitrarily large period. We conjecture that there exist starting conditions which do not lead to tunnels, justify the conjecture with simulation evidence, and discuss the difficulty of proving it.