Pseudorandom Number Generation in the Context of a 3D Simulation Model for Tissue Growth

In this paper, we consider our choice of a pseudorandom number generator (PRNG) in the context of running a simulation model for the growth of 3D tissues. This PRNG is the multiplicative linear congruential generator (MLCG) with carefully chosen parameters. We base our selection of this generator on three criteria. They are periodicity, randomness quality, and ease of implementation. In these regards, we review some of the pertinent theoretical properties of the employed MLCG and describe techniques used to obtain such sequences serially. Our investigation indicates that the MLCG, with properly selected parameters, can be a good, portable, user-specified, and user-controlled generator with acceptable quality. During the simulation of tissue growth, our various experiments have also shown that the ratio of the total number of random numbers consumed till confluence to the total number of computational sites in the cellular array never exceeds a certain number. This number can be used as a predictor for the period of a PRNG needed to run a particular experiment to simulate tissue growth and to estimate when a longer period may be required in order to deal with very large data sets