Upper bounds for the Hausdorff dimension of Weierstrass curves

TL;DR

This paper derives a computable upper bound for the Hausdorff dimension of Weierstrass curves using hyperbolic iterated function systems, offering a new approach despite being weaker than previous results.

Contribution

It introduces a new method to estimate the Hausdorff dimension of Weierstrass curves based on hyperbolic iterated function systems, which is directly computable.

Findings

Provides an upper bound for Hausdorff dimension of Weierstrass curves

The bound is weaker than existing results but more computationally accessible

Uses hyperbolic iterated function systems for the estimation

Abstract

We produce an upper bound for the Hausdorff dimension of the graph of a Weierstrass-type function. Whilst strictly weaker than existing results, it has the advantage of being directly computable from the theory of hyperbolic iterated function systems.