In this paper, we attempt to define and understand the orbits of the Koch
snowflake fractal billiard $KS$. This is a priori a very difficult problem
because $\partial(KS)$, the snowflake curve boundary of $KS$, is nowhere
differentiable, making it impossible to apply the usual law of reflection at
any point of the boundary of the billiard table. Consequently, we view the
prefractal billiards $KS_n$ (naturally approximating $KS$ from the inside) as
rational polygonal billiards and examine the corresponding flat surfaces of
$KS_n$, denoted by $\mathcal{S}_{KS_n}$. In order to develop a clearer picture
of what may possibly be happening on the billiard $KS$, we simulate billiard
trajectories on $KS_n$ (at first, for a fixed $n\geq 0$). Such computer
experiments provide us with a wealth of questions and lead us to formulate
conjectures about the existence and the geometric properties of periodic orbits
of $KS$ and detail a possible plan on how to prove such conjectures.