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.
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