Solar flare cellular automata interpreted as discretized MHD equations

We show that the Cellular Automaton (CA) model for Solar flares of Lu and Hamilton (1991) can be understood as the solution to a particular partial differential equation (PDE), which describes diffusion in a localized region in space if a certain instability threshold is met, together with a slowly acting source term. This equation is then compared to the induction equation of MHD, the equation which governs the energy release process in solar flares. The similarities and differences are discussed. We make some suggestions how improved Cellular Automaton models might be constructed on the basis of MHD, and how physical units can be introduced in the existing respective Cellular Automaton models. The introduced formalism of recovering equations from Cellular Automata models is rather general and can be applied to other situations as well.