el os Keywords: Agent-based simulation

co uum hese tion sources are the choice of limiting arguments, the use of a discrete-time model as opposed to a continu-iting regime that accurately approximates the conservation equation for the cellular automata, we are te age agent As such compo literature extensively considers discrete-time CA models [1,4–6,11,18,22,23], in particular when deriving approximations to the average behaviour of these processes, and so we begin our analysis with discrete-time CA models in Section 2 before considering continuous-time CA models in Section 3. Of much interest from both a practical and theoretical perspec-tive, is the derivation of approximations which capture the average ir derivation, and ped when these ndence be the state of different sites in the CA is a key issue regards to the inaccuracy of existing continuum appr tions, so long as proliferation is present; and that, when is no proliferation, the approximation obtained by assuming independence is identical to that found when the independence assumption is relaxed. However, the earlier continuum models are shown to perform unexpectedly well in approximating the behaviour of the CA even when proliferation is included. We show that this is largely due to a fortuitous cancellation of errors