The roughness of the core-mantle boundary, on the scale of centimeters to tens of meters, is modelled using a cellular automata method. Square cells, of the size of grains of the mantle material, on a 2-D grid, can be in one of three states corresponding to mantle silicate or oxide, core fluid saturated in light element and unsaturated core fluid. The dynamical process of evolution is defined as a stationary stochastic process without memory. Transitions of doublets of cells from one state to another are governed by parameters representing the rates of physical processes: dissolution and crystallization at the CMB and diffusion of the light element in the core fluid. With reasonable values of the parameters, the boundary roughens on the scale of grains, and a boundary layer of saturated fluid, of a few tens of centimeters thick, soon appears at the interface. An undulation with dominant wavelength of the order of a few tens of meters eventually appears. An interaction of the roughness of the CMB with the fluid flow in the core is considered as possible.
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