Jg. Stevens et al., TRANSIENT AND CYCLIC BEHAVIOR OF CELLULAR-AUTOMATA WITH NULL BOUNDARY-CONDITIONS, Journal of statistical physics, 73(1-2), 1993, pp. 159-174
One-dimensional cellular automata (CA) over finite fields are studied
in which each interior cell is updated to contain the sum of the previ
ous values of its two nearest neighbors. Boundary cells are updated ac
cording to null boundary conditions. For a given initial configuration
, the CA evolves through transient configurations to an attracting cyc
le. The dependence of the maximal transient length and maximal cycle l
ength on the number of cells is investigated. Both can be determined f
rom the minimal polynomial of the update matrix, which in this case sa
tisfies a useful recurrence relation. With cell values from a field of
characteristic two, the explicit dependence of the maximal transient
length on the number of cells is determined. Extensions and directions
for future work are presented.