On the constancy regions for mixed test ideals

In this note we study the partition of R⩾0n given by the regions where the mixed test ideals τ(a1t1…antn) are constant. We show that each region can be described as the preimage of a natural number under a p-fractal function φ:R⩾0n→N. In addition, we give some examples illustrating that these regions do not need to be composed of finitely many rational polytopes.