# Spectral Properties of Laplacians on Snowflake domains and filled Julia sets

## TL;DR

This paper investigates the spectral properties of Laplacians on snowflake fractals and filled Julia sets, providing eigenvalue data, visualizations, and geometric measurements to understand their spectral behavior.

## Contribution

It offers new eigenvalue data, visualizations of eigenfunctions, and geometric approximations for fractals and Julia sets, linking spectral properties with fractal geometry.

## Key findings

- Eigenvalue data and eigenfunction images for snowflake and Julia sets.
- Approximate area and box-counting dimension of Julia sets.
- Comparison of eigenvalue counting function with Weyl's law.

## Abstract

We present eigenvalue data and pictures of eigenfunctions of the classic and quadratic snowflake fractal and of quadratic filled Julia sets. Furthermore, we approximate the area and box-counting dimension of selected Julia sets to compare the eigenvalue counting function with the Weyl term.