Spatial spectrum of a general family of self-similar arrays

Abstract

We describe the structure factors of a fairly general family of self-similar deterministic arrays (fractals). These are constructed recursively by an inflation method which imitates real physical processes where large clusters are grown from smaller entities. An algebraic approach is used to describe the behavior of the structure factors in the limit of arbitrarily large objects. These structure factors exhibit several scaling properties which reflect the self-similarity of the direct space arrays.