Abstract
In the past, cellular automata based models and machines [ The Theory of Self-Reproducting Automata, University of Illinois Press, Urbana, 1996; Rev. Mod. Phys. 55 (1983) 601; Am. Math. Month. 97 (1990) 24; Matrix and Linear Algebra, Prentice-Hall, India, 1991; TRE Trans. Circuits CT-6 (1959) 45; Cellular Automata Machines, MIT Press, Cambridge, 1987] were proposed for simulation of physical systems, but without any analytical insight into the behaviour of the underlying simulation process. The set of papers [Int. J. Comput. Math. Appl. 33 (1997) 79; Int. J. Comput. Math. Appl. 37 (1999) 115; Matrix algebraic formulae concerning a particular rule of two dimensional cellular automata, Inf. Sci., submitted] made a significant departure from this traditional approach. In the mentioned papers, a simple and precise mathematical model using matrix algebra built on GF(2) was reported for characterising the behaviour of two-dimensional nearest neighbourhood linear cellular automata with null and periodic boundary conditions. As a sequel, in the present paper an attempt has been made to characterise a number of exceptional transformations or rules, each of which behaving uniquely, not matching with any other rules. Thus this set of exceptional rules demand special attention.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call