  A set-up is introduced which can be superimposed onto the existing solar
flare cellular automata (CA) models, and which specifies the interpretation of
the model's variables. It extends the CA models, yielding the magnetic field,
the current, and an approximation to the electric field, in a way that is
consistent with Maxwell's and the MHD equations. Applications to several solar
flare CA models during their natural state (self-organized criticality (SOC))
show, among others, that (1) the magnetic field exhibits characteristic
large-scale organization over the entire modeled volume; (2) the magnitude of
the current seems spatially dis-organized, with no obvious tendency towards
large-scale structures or even local organization; (3) bursts occur at sites
with increased current, and after a burst the current is relaxed; (4) by
estimating the energy released in individual bursts with the use of the current
as Ohmic dissipation, it turns out that the power-law distributions of the
released energy persist. The CA models, extended with the set-up, can thus be
considered as models for energy-release through current-dissipation. The
concepts of power-law loading and anisotropic events (bursts) in CA models are
generalized to 3--D vector-field models, and their effect on the magnetic field
topology is demonstrated.
