Year: 2026
Type: preprint
Abstract: In this article, we first investigate the box dimension results for the graphs of continuous functions defined on $\mathfrak{F\times F}$, where $\mathfrak{F}$ is the self-similar fractal generated by an iterated function system (IFS) exhibiting the open set condition (OSC). Following this, we manifest the existence of a prevalent surface, defined by a continuous function on $\mathfrak{F\times F}$, that satisfies the horizon property in relation to the box dimension, i.e., the box dimension of the prevalent surface is greater than that of its horizon up to a constant $η$, where $η$ is the box dimension of the self-similar fractal $\mathfrak{F}$. Finally, we provide an example consolidating that the OSC on the underlying IFS of $\mathfrak{F}$ cannot be dropped.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Ministry of Education, India
OpenAlex ID: W7204071805