Bitwise Implementation of a Two-Dimensional Cellular Automata Biofilm Model

Abstract

Mathematical modeling using the cellular automata (CA) approach is an attractive alternative to models based on partial differential equations when the domains to be simulated have complex boundary conditions. The computational efficiency of CA models is readily observed when using parallel processors, but implementations in personal computers are, although feasible, not quite efficient. In an effort to improve the computational efficiency of CA implementations in personal computers, we introduce in this paper a bitwise implementation based on the use of each bit as a different CA cell. Thus, in a 32-bit processor, each computer word stores information about 32 different CA cells. We illustrate the bitwise implementation with a biofilm model that simulates substrate diffusion and microbial growth of a single-species, single-substrate, structurally heterogeneous biofilm. The efficiency of the bitwise implementation was evaluated by comparing the computational time of equivalent CA biofilm models that used more common low-level implementations, namely, if-then operators and look-up tables. The processing speed of the bitwise implementation was over an order of magnitude higher than the processing speed of the other two implementations. Regarding the biofilm simulations, the CA model exhibited self-organization of the biofilm morphology as a function of kinetic and physical parameters.