FPGA implementations of the RNR cellular automata to model electrostatic field

The classic way to describe electrostatic field is using Partial Differential Equations and suitable boundary conditions. In most situations we need numerical methods mainly based on discretisation of time and space. In this paper we follow a different approach: we introduce RNR Cellular Automata that is capable of modeling the electrostatic field at macroscopic level. Iterations of the automata are averaged on time and space to get continuous variables. We implement RNR Cellular Automata with FPGA and compare the performance with the results using classic sequential programming. We get some regular architectures specially adapted to fully-parallel machines, and explore its benefits and drawbacks.