  Equation-based simulations are most commonly used in the physical sciences and other sciences where there is governing theory that can guide the construction of mathematical models based on differential equations. I use the term “equation based” here to refer to simulations based on the kinds of global equations we associate with physical theories—as opposed to “rules of evolution” (which are discussed in the next section.) Equation based simulations can either be particle-based, where there are n many discrete bodies and a set of differential equations governing their interaction, or they can be field-based, where there is a set of equations governing the time evolution of a continuous medium or field. An example of the former is a simulation of galaxy formation, in which the gravitational interaction between a finite collection of discrete bodies is discretized in time and space.  An example of the latter is the simulation of a fluid, such as a meteorological system like a severe storm. Here the system is treated as a continuous medium—a fluid—and a field representing its distribution of the relevant variables in space is discretized in space and then updated in discrete intervals of time.