  Fibonacci chains are special diatomic, harmonic chains with uniform nearest
neighbour interaction and two kinds of atoms (mass-ratio $r$) arranged
according to the self-similar binary Fibonacci sequence $ABAABABA...$, which is
obtained by repeated substitution of $A \to AB$ and $B \to A$. The implications
of the self-similarity of this sequence for the associated orthogonal
polynomial system which govern these Fibonacci chains with fixed mass-ratio $r$
are studied.
