A simple numerical model of the self-excitation of the magnetic field by chaotic motion of a highly conductive fluid is being developed. It is based on the following approach to simulating the turbulent dynamo generation of magnetic fields: the fluid is divided into cells and each cell acts as a machine that can randomly amplify or destroy a given magnetic field. The random amplification models the effects of a chaotic fast dynamo and the random destruction models the effects of reconnection. Uncorrelated and correlated processes are considered. Effects of non-linearity, diffusion, and correlation between cells in time and space are also included. Numerical results are presented from one- and two-dimensional models and possible applications to the generation and spatial-temporal distribution of solar, planetary and interplanetary magnetic fields are discussed.