Magnetic topology, heating rates, and the formation of the millimeter continuum in a three-dimensional radiative-magnetohydrodynamics simulation. Panel A: photospheric magnetogram clipped at ±1 kG; the yellow shade shows where T_b [3mm]> 9 kK. The area inside the dotted box is displayed in panels B and C, which show T_b [3mm] and the sum of viscous and resistive heating integrated within the CF of the 3 mm continuum. The group of panel D show from the left to the right: current density squared per mass unit (square-root scaling), logarithm of temperature, and CF_3 mm slices along the dotted paths S1 and S2 overlaid on panels B and C; the white dashed lines show where τ_3 mm = 1, and the dotted black lines show where CF is at 1% of the maximum in each column.