A (deterministic) substitution consists of a finite alphabet along with a set of transformation rules. A classical example is the Fibonacci substitution, which is composed of the transformations taking a to ab and b to a. Deterministic and random substitutions have associated dynamical systems and invariant measures, which capture certain “asymptotic statistics” of the substitution.
In my joint paper with Andrew Mitchell, we study the multifractal properties of measure associated with random substitutions.
- Multifractal analysis of measures arising from random substitutions
With: Andrew Mitchell Journal: Preprint (submitted) Links: pdfarxiv