Random number generators (RNGs) based upon neighborhood-of-four cellular automata (CA) with asymmetrical, non-local connections are explored. A number of RNGs that pass Marsaglia's rigorous Diehard suite of random number tests have been discovered. A neighborhood size of four allows a single CA cell to be implemented with a four-input lookup table and a one-bit register which are common building blocks in popular field programmable gate arrays (FPGAs). The investigated networks all had periodic (wrap around) boundary conditions with either 1-d, 2-d, or 3-d interconnection topologies. Trial designs of 64-bit networks using a Xilinx XCV1000-6 FPGA predict a maximum clock rate of 214 MHz to 230 MHz depending upon interconnection topology.
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