We develop a new version of a Cellular Automaton (CA) for the simulation of the dynamics of a stellar atmosphere sitting on top of an inert core, and specified by the following physical input parameters: mass, radius and luminosity of core, and mass of atmosphere. The CA incorporates various parametrised simulation schemes of the instability mechanism (essentially ionisation). The initial state in all of our numerical experiments is a radially symmetric atmosphere of exponential density run and uniform temperature (input parameters: density scale– height and temperature of atmosphere). The initial atmosphere is not in hydrostatic and thermal equilibrium. After a transient stage, the system relaxes, for certain ranges of the parameters of the instability mechanism, towards a state of nontrivial dynamical behaviour: Local heat–driven circulations are set up which may range from nearly stationary and spatially symmetric cellular patterns to temporally and spatially irregularly fluctuating velocity fields. The traditional radial symmetry of the density pattern is broken, so that the star acquires a globally non–spherical shape. The residual non–stationary component, when integrated over the star to produce the counterpart of an observational velocity curve of a variable star, shows an irregular cyclic behaviour which does not have the signature of low–dimensional deterministic chaos.