In 1994 George Willis introduced the scale function for
automorphisms of locally compact totally disconnected groups.
These groups are very close to algebra, having a local base at
the neutral element formed by open compact subgroups (a p-adic
Lie group must be a leading example). The aim of this talk is to
introduce this function and the compare it with the entropy
(both algebraic and topological) of such an automorphism.