3 papers
math.DS2025
Two-scale branching functions and inhomogeneous attractors
Vilma Orgoványi, Alex Rutar
We introduce the notion of a two-scale branching function associated with an arbitrary metric space, which encodes the lower and upper box dimensions as well as the Assouad spectru…
math.MG2024
On the uniformity and size of microsets
Richárd Balka, Vilma Orgoványi, Alex Rutar
We resolve a few questions regarding the uniformity and size of microsets of subsets of Euclidean space. First, we construct a compact set with Assouad dimen…
math.DS2022
Projections of the random Menger sponge
Károly Simon, Vilma Orgoványi
Using a similar random process to the one which yields the fractal percolation sets, starting from the deterministic Menger sponge we get the random Menger sponge. We examine its o…