  Hydrodynamic and magnetohydrodynamic convective attractors in
three-dimensional rotating Rayleigh-B\'enard convection are studied numerically
by varying the Taylor and Rayleigh numbers as control parameters. First, an
analysis of hydrodynamic attractors and their bifurcations is conducted, where
routes to chaos via quasiperiodicity are identified. Second, the behaviour of
the magnetohydrodynamic system is investigated by introducing a seed magnetic
field and measuring its growth or decay as a function of the Taylor number,
while keeping the Rayleigh number fixed. Analysis of the attractors shows that
rotation has a significant impact on magnetic field generation in
Rayleigh-B\'enard convection, with the critical magnetic Prandtl number
changing nonmonotonically with the rotation rate. It is argued that a
nonhysteretic blowout bifurcation with on-off intermittency is responsible for
the transitions to dynamo.
