Fine-grained parallel models of spatial dynamics are analyzed from the point of view of the relationship between their continuous and discrete constituents. The models are ranged from the absolutely continuous partial differential equations to the absolutely discrete cellular automata. In the interval between them, there are cellular neural networks, cellular neural automata, and probabilistic cellular automata. A generalized representation of the above models is proposed, which is assumed to be a background for a unified technology for the fine-grained parallel programming. The models are analyzed and compared on the basis of the results, obtained at the Supercomputer Software Department.