In this paper, we attempt to define and understand the orbits of the Kochsnowflake fractal billiard $KS$. This is a priori a very difficult problembecause $\partial(KS)$, the snowflake curve boundary of $KS$, is nowheredifferentiable, making it impossible to apply the usual law of reflection atany point of the boundary of the billiard table. Consequently, we view theprefractal billiards $KS_n$ (naturally approximating $KS$ from the inside) asrational polygonal billiards and examine the corresponding flat surfaces of$KS_n$, denoted by $\mathcal{S}_{KS_n}$. In order to develop a clearer pictureof what may possibly be happening on the billiard $KS$, we simulate billiardtrajectories on $KS_n$ (at first, for a fixed $n\geq 0$). Such computerexperiments provide us with a wealth of questions and lead us to formulateconjectures about the existence and the geometric properties of periodic orbitsof $KS$ and detail a possible plan on how to prove such conjectures.
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