In the past, Cellular Automata based models and machines [1] have been
proposed for simulation of physical systems without any analytical in
sight into the behaviour of the underlying simulation machine. This pa
per makes a significant departure from this traditional approach. An e
legant mathematical model using simple matrix algebra is reported in t
his paper for characterizing the behaviour of two-dimensional nearest
neighbourhood linear cellular automata with null and periodic boundary
conditions. Based on this mathematical model, a VLSI architecture of
a Cellular Automata Machine (CAM) has been proposed. Interesting appli
cations of CAM in the fields of image analysis and fractal image gener
ation are also reported.