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\section{A physical model}  Underlying all simulations is a physical model that describes the world, and the movement of sheep in particular.  \subsection{The world}  The world is modeled as a box, $[0, x_{m}]\times[0,y_{m}]$.   We can represent the sheep, dogs and target(s) as points.   We choose not to discretize the space, since that allows for more prolific movement, a more realistic environment, and a more interesting modeling perspective.  \subsection{Physics of sheep}  Here, we get our inspiration from Boids \cite{boids}, and define the following axioms for  movement of sheep.