  Solar observations with the Atacama Large Millimeter/sub-millimeter Array
(ALMA) facilitate studying the atmosphere of the Sun at chromospheric heights
at high spatial and temporal resolution at millimeter wavelengths. ALMA
intensity data at mm-wavelengths are used for a first detailed systematic
assessment of the occurrence and properties of small-scale dynamical features
in the quiet Sun. ALMA Band 3 data (~ $3$ mm / $100$ GHz) with spatial
resolution ~ $1.4$ - $2.1$ arcsec and a duration of ~ $40$ min are analysed
together with SDO/HMI magnetograms. The temporal evolution of the mm-maps is
studied to detect pronounced dynamical features which are connected to
dynamical events via a k-means clustering algorithm. The physical properties of
the resulting events are studied and it is explored if they show properties
consistent with propagating shock waves. For this purpose, observable shock
wave signatures at mm wavelengths are calculated from one- and
three-dimensional model atmospheres. There are 552 dynamical events detected
with an excess in brightness temperature ($\Delta T_\text{b}$) of at least
$\geq 400$ K. The events show a large variety in size up to ~ $9$ arcsec,
amplitude $\Delta T_\text{b}$ up to ~ $1200$ K with typical values between ~
$450$ - $750$ K and lifetime at FWHM of $\Delta T_\text{b}$ between ~ $43$ -
$360$ s, with typical values between ~ $55$ - $125$ s. Furthermore, many of the
events show signature properties that suggest that they are likely produced by
propagating shock waves. There are a lot of small-scale dynamic structures
detected in the Band 3 data, even though the spatial resolution sets
limitations of the size of events that can be detected. The amount of dynamic
signatures in the ALMA mm data is very low in areas with photospheric
footpoints with stronger magnetic fields, which is consistent with the
expectation for propagating shock waves.
