Hydrodynamic and magnetohydrodynamic convective attractors in a plane horizontal layer are investigated numerically. We consider Boussinesq Rayleigh-Benard convection assuming stress-free boundary conditions on horizontal boundaries and periodicity in horisontal directions. For the considered parameters fifteen different types of hydrodynamic attractors are found, out of which only 6 can act as kinematic dynamos. The final magnetohydrodynamic attractors are either quasiperiodic or chaotic.