A Family of Fibonacci Lattices

Abstract

A variety of Fibonacci lattices, which are locally isomorphic each other and satisfy Conway’s theorem, is found to exist through the projection method by changing the location of the window in the square lattice. The structure of each system, described by a (semi-infinite) series of the Fibonacci generations, is characterized by its own cycle, i.e. its own self-similarity. On the wave function at E=0 in an off-diagonal model (for example), the family yields a variety of multi-fractal distributions.