  We investigate, theoretically and experimentally,the properties of
diffraction spectra of Fibonacci lattices with arbitrary spacings. We show
that, by means of a suitable composition rule, a Fibonacci sequence can be
mapped into another one with a different lattice spacing. In this way we are
able to define equivalence classes of Fibonacci structures and their
generators, namely the Fibonacci sequences from which all the others can be
obtained by compostion rule. We show that each class can be characterized by a
given diffraction pattern which is essentially the one of the generator, in the
sense that the most prominent features of this spectrum are common to all the
elements of the class. This theoretical prediction is in good agreement with
experimental results.
