  The initial conditions for the mass loss during the asymptotic giant branch
(AGB) phase are set in their extended atmospheres, where, among others,
convection and pulsation driven shocks determine the physical conditions. High
resolution observations of AGB stars at (sub)millimetre wavelengths can now
directly determine the morphology, activity, density, and temperature close to
the stellar photosphere. We used the Atacama Large Millimeter/submillimeter
Array (ALMA) high angular resolution observations to resolve the extended
atmospheres of four of the nearest AGB stars: W Hya, Mira A, R Dor and R Leo.
We interpreted the observations using a parameterised atmosphere model. We
resolve all four AGB stars and determine the brightness temperature structure
between $1$ and $2$ stellar radii. For W Hya and R Dor we confirm the existence
of hotspots with brightness temperatures $>3000$ to $10000$~K. All four stars
show deviations from spherical symmetry. We find variations on a timescale of
days to weeks, and for R Leo we directly measure an outward motion of the
millimetre wavelength surface with a velocity of at least
$10.6\pm1.4$~km~s$^{-1}$. For all objects but W Hya we find that the
temperature-radius and size-frequency relations require the existence of a
(likely inhomogeneous) layer of enhanced opacity. The ALMA observations provide
a unique probe of the structure of the extended AGB atmosphere. We find highly
variable structures of hotspots and likely convective cells. In the future,
these observations can be directly compared to multi-dimensional chromosphere
and atmosphere models that determine the temperature, density, velocity, and
ionisation structure between the stellar photosphere and the dust formation
region. However, our results show that for the best interpretation, both very
accurate flux calibration and near-simultaneous observations are essential.
