Recursive procedures for measuring disorder in non-periodic sequences and lattices

Recursive procedures are developed for calculating the conditional probabilities and kth-order entropy for non-periodic sequences and lattices. The entropies are used to provide a measure of disorder and this paper generalizes previous work in two ways: the use of three or more different atoms in the chain; providing a measure for disorder in a lattice constructed from non-periodic sequences. In addition, a quantitative comparison of the disorder in the Fibonacci and Thue-Morse sequences with three different types of atom is discussed.