Magnetic fields of planets and other astrophysical objects are often sustained by conducting fluid motions, driven by convection in their interior. A common feature of such objects is rotation. This work is aimed at investigation of magnetic field generation in an idealized setup. We consider a rotating conducting fluid heated from below in a plane horizontal layer (often regarded as representing a segment of a spherical shell in the interior of a planet). Flows and magnetic fields in square periodicity cells are examined for the aspect ratio, for which the trivial hydrodynamic steady state becomes unstable to square patterns at the minimal Rayleigh number. All hydrodynamic attractors in a certain region of parameter values are found numerically. To study the influence of rotation on the structure of the hydrodynamic attractors, we are varying the Taylor number from Ta=0 (no rotation) to Ta=2000 (Coriolis force suppresses the fluid motion) with the fixed other parameters of the system. Magnetic field generation in the kinematic regime by the attracting fluid flows is examined. Magnetic field generation in the nonlinear regime is studied. The problem is investigated numerically by
standart pseudospectral methods and a fast algorithm for integration in time of the Fourier-Galerkin system of ODE's.