5 papers
Calculating box dimension with the method of types
István Kolossváry
This paper presents a general procedure based on using the method of types to calculate the box dimension of sets. The approach unifies and simplifies multiple box counting argumen…
On the intermediate dimensions of Bedford-McMullen carpets
István Kolossváry
The intermediate dimensions of a set , elsewhere denoted by , interpolates between its Hausdorff and box dimensions using the parameter . Determining a preci…
Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line
Balázs Bárány, István Kolossváry, Michał Rams +1
This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generic…
Triangular Gatzouras-Lalley-type planar carpets with overlaps
István Kolossváry, Károly Simon
We construct a family of planar self-affine carpets with overlaps using lower triangular matrices in a way that generalizes the original Gatzouras--Lalley carpets defined by diagon…
The Prime Grid. Introducing a geometric representation of natural numbers
István Kolossváry
In this report we present an off-the-number-line representation of the positive integers by expressing each integer by its unique prime signature as a grid point of an infinite dim…