  Studying systems where many individual bodies in motion interact with one
another is a complex and interesting area. Simple mechanisms that may be
determined for biological, chemical, or physical reasons can lead to
astonishingly complex results that require a further understanding of the
moving bodies. With the increasing interaction between computation and various
scientific areas, it has become more useful, feasible, and important to create
models for these systems. Here, we present two families of models,
deterministic and nondeterministic, along with three distinct and realistic
interaction mechanisms. These are combined in a unique way to provide the
groundwork for particle system models across multiple disciplines. This work
has applications that range from biology to chemistry and physics. In addition
to describing the motivations and math behind all the models, software is
provided that allows researchers to quickly adjust and implement what is
described here.
