Context :

Aims : In this work we investigate the dynamic behavior of inter-network regions of the solar chromosphere .

Methods : We observed the chromosphere of the quiet Sun using a narrow-band Lyot filter centered at the Ca ii K _ { \mathrm { 2 v } } emission peak with a bandpass of 0.3 Å .
We achieved a spatial resolution of on average 0 \aas@@fstack { \prime \prime } 7 at a cadence of 10 s .

Results : In the inter-network we find a mesh-like pattern that features bright grains at the vertices .
The pattern has a typical spatial scale of 1 \aas@@fstack { \prime \prime } 95 and a mean evolution time scale of 53 s with a standard deviation of 10 s. A comparison of our results with a recent three-dimensional radiation hydrodynamical model implies that the observed pattern is of chromospheric origin .
The measured time scales are not compatible with those of reversed granulation in the photosphere although the appearance is similar .
A direct comparison between network and inter-network structure shows that their typical time scales differ by at least a factor of two .

Conclusions : The existence of a rapidly evolving small-scale pattern in the inter-network regions supports the picture of the lower chromosphere as a highly dynamical and intermittent phenomenon .