What a bunch of nerds!
I can't believe I hang out here.
On factor in the distribution of shot patterns is that in the early phases of blast, there is a significant laminar flow effect (Hagen–Poiseuille) especially in smaller bore shotguns. In theory, this should only apply to "fluids", but it creates a decent approximation of a "matrix" of gasses, powder by-products and shot moving at speed. In fact, the "choke" on a shotgun is more about an instantaneous application of the turbulence that increases as the 4th power of the radius shrinkage (the most extreme exponential factor I have ever used in a normal physics engine).
After the shot is roughly two barrel lengths away from the shotgun, all laminar flow effects seem to diminish to zero and each pellet is on its own path.
Oh, by the way, Welcome from the Free State of Nevada and all that. Glad to have you on the forum.