  The chromosphere in internetwork regions of the quiet Sun was regarded as a
static and homogeneous layer for a long time. Thanks to advances in
observations and numerical modelling, the wave nature of these atmospheric
regions received increasing attention during the last decade. Recent
three-dimensional radiation magnetohydrodynamic simulations with CO5BOLD
feature the chromosphere of internetwork regions as a dynamic and intermittent
phenomenon. It is a direct product of interacting waves that form a mesh-like
pattern of hot shock fronts and cool post-shock regions. The waves are excited
self-consistently at the top of the convection zone. In the middle chromosphere
above an average height of 1000 km, plasma beta gets larger than one and
magnetic fields become more important. The model chromosphere exhibits a
magnetic field that is much more homogeneous than in the layers below and
evolves much faster. That includes fast propagating (MHD) waves. Further
improvements of the simulations like time-dependent hydrogen ionisation are
currently in progress. This class of models is capable of explaining apparently
contradicting diagnostics such as carbon monoxide and UV emission at the same
time.
