A Fibonacci quasicrystal is a model used in theoretical studies of quasicrystals. Its elements are arranged in one or more spatial dimensions according to the sequence given by the Fibonacci word. The Fourier transform of such arrangements consist of discrete values, which is the defining property for crystals.
A Fibonacci sequence is the result of a recursive iteration, which repeats a structural pattern with a small difference. This aspect of deflationary construction by difference and repetition is also implicit in a quasicrystal. In fact, if we use only two symbols for the starting points of the sequence ( instead of adding numbers ) and form a chain with the same rule, the relation becomes visible.
In an algebric form the sequence is expressed with a matrix whose eigenvalues are Pisot numbers. This feature guarantees that its Fourier transform is discrete. Interpreted in physical terms this amounts to say that the structure would produce Bragg peaks.