This paper is concerned with the mathematical characterization and wavelet analysis of self-similar random
vector fields. The study consists of two main parts: the construction of random vector models on the basis of
their invariance under coordinate transformations, and a study of the consequences of conducting a wavelet
analysis of such random models. In the latter part, after briefly examining the effects of standard wavelets on
the proposed random fields, we go on to introduce a new family of Laplacian-like vector wavelets that in a
way duplicate the covariant-structure and whitening relations governing our random models.