Optimal parametrizations of a class of self-affine sets

In this paper, we study optimal parametrizations of the invariant sets of a single matrix graph IFS which is a generalization of the result of Rao and Zhang (2016). We show that the invariant sets of a linear single matrix GIFS which has a primitive associated matrix and satisfies the open set condition admit optimal parametrizations. This result is the basis of the further study of space-filling curves of self-affine sets.