The increasing power of computers makes it possible to model the nonlinear interaction between magnetic fields and convection at the surfaces of solar-type stars in ever greater detail. We present the results of idealized numerical experiments on two-dimensional magnetoconvection in a fully compressible perfect gas. We first vary the aspect ratio lambda of the computational box and show that the system runs through a sequence of convective patterns, and that it is only for a sufficiently wide box (lambda>=6) that the flow becomes insensitive to further increases in lambda. Next, setting lambda=6, we decrease the field strength from a value strong enough to halt convection and find transitions to small-scale steady convection, next to spatially modulated oscillations (first periodic, then chaotic) and then to a new regime of flux separation, with regions of strong field (where convection is almost completely suppressed) separated by broad convective plumes. We also explore the effects of altering the boundary conditions and show that this sequence of transitions is robust. Finally, we relate these model calculations to recent high-resolution observations of solar magnetoconvection, in plage regions as well as in light bridges and the umbrae of sunspots. \u
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