  We investigate numerically magnetic field generation by thermal convection
with square periodicity cells in a rotating horizontal layer of
electrically-conducting fluid with stress-free electrically perfectly
conducting boundaries for Rayleigh numbers in the interval 5100\le R\le 5800.
Dynamos of three kinds, apparently not encountered before, are presented: 1)
Steady and time-periodic regimes, where the flow and magnetic field are
symmetric about a vertical axis. In regimes with this symmetry, the global
alpha-effect is insignificant, and the complex structure of the system of
amplitude equations controlling weakly nonlinear stability of the system to
perturbations with large spatial and temporal scales suggests that the
perturbations are likely to exhibit uncommon complex patterns of behaviour, to
be studied in the future work. 2) Periodic in time regimes, where magnetic
field is always concentrated in the interior of the convective layer, in
contrast to the behaviour first observed by St Pierre (1993) and often
perceived as generic for electrically infinitely conducting boundaries. 3) A
dynamo exhibiting chaotic behaviour of heteroclinic nature, where a sample
trajectory enjoys excursions between a periodic magnetohydrodynamic regime and
rolls. The rolls are amagnetic, but generate magnetic field kinematically. As a
result, magnetic energy falls off almost to zero, while the rolls are
approached.
