  Interpretation of imagery of the solar chromosphere in the widely used
\CaIIIR infrared line is hampered by its complex, three-dimensional and non-LTE
formation. Forward modelling is required to aid understanding. We use a 3D
non-LTE radiative transfer code to compute synthetic \CaIIIR images from a
radiation-MHD simulation of the solar atmosphere spanning from the convection
zone to the corona. We compare the simulation with observations obtained with
the CRISP filter at the Swedish 1--m Solar Telescope. We find that the
simulation reproduces dark patches in the blue line wing caused by Doppler
shifts, brightenings in the line core caused by upward-propagating shocks and
thin dark elongated structures in the line core that form the interface between
upward and downward gas motion in the chromosphere. The synthetic line core is
narrower than the observed one, indicating that the sun exhibits both more
vigorous large-scale dynamics as well as small scale motions that are not
resolved within the simulation, presumably owing to a lack of spatial
resolution.
