Self-Similar Hierarchical Regular Lattices

This paper deals with the topological-metric structure of a network made by a family of self-similar hierarchical regular lattices. We derive the basic properties and give a suitable definition of self-similarity on lattices. This concept of self-similarity is shown on some classical (omothety) and more recent models (Sierpinski tesselations and Husimi cacti). Both the metric and the geometric properties of the lattice will be intrinsically defined