  Sometimes the step-by-step methods of computer simulation are used because the model of interest contains continuous (differential) equations (which specify continuous rates of change in time) that cannot be solved analytically—either in principle or perhaps only in practice. This underwrites the spirit of the following definition given by Paul Humphreys: “any computer-implemented method for exploring the properties of mathematical models where analytic methods are not available” (1991, 500). But even as a narrow definition, this one should be read carefully, and not be taken to suggest that simulations are only used when there are analytically unsolvable equations in the model. Computer simulations are often used either because the original model itself contains discrete equations—which can be directly implemented in an algorithm suitable for simulation—or because the original model consists of something better described as rules of evolution than as equations.