Heating rates and the formation of the millimeter continuum in the simulation. Panel A: integrated j²/ρ weighted by the contribution function of the 3 mm continuum (CF_3 mm). Panel B: photospheric magnetogram (range ±1 kG) with three-dimensional rendering of magnetic field lines and CF_3 mm (blue shade) of the region indicated by the arrow in panel A. A threshold was applied to the CF values not to hide the field lines. Panel C: height at which τ = 1 at 3 mm; the errorbar overlaid on the colormap shows the median and the range between the 16th and 84th percentiles of the distribution. Panel D: temperature (dashed lines), total heating rates per mass (yellow lines), and CF_3 mm (blue lines) as a function of height at two locations indicated in panels A and C.