R. Dániel Prokaj | Searcharxiv

arXiv2026

On the revolving structure of the Lévy dragon and its linear transforms

Lévy's Dragon Curve is a well-known self-similar fractal, notable for its ability to tile the complex plane. We review a representation of the curve as a set of points given by complex power series satisfying a revolving condition, and study how this representation changes under linear transformations, while preserving its characteristic geometric properties. We introduce a labeled directed graph that encodes these series representations and show that this directed graph remains invariant under linear transformations, with only the labeling subject to change. Furthermore, we provide a geometric characterization of the resulting variations in graph labeling.

math.CA↗

arXiv2025

On the dimension theory of Okamoto's function

In this paper, we investigate the dimension theory of the one parameter family of Okamoto's function. We compute the Hausdorff, box-counting and Assouad dimensions of the graph for a typical choice of parameter. Furthermore, we study the dimension of the level sets. We give an upper bound on the dimension of every level set, and we show that for a typical choice of parameters this value is attained for Lebesgue almost every level sets.

math.DS↗