TRANSIENT AND CYCLIC BEHAVIOR OF CELLULAR-AUTOMATA WITH NULL BOUNDARY-CONDITIONS

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.