# Transcendental Julia Sets with Fractional Packing Dimension

## TL;DR

This paper constructs new examples of transcendental entire functions with Julia sets having packing dimensions strictly between 1 and 2, demonstrating the diversity of fractal dimensions in complex dynamics.

## Contribution

It introduces the first known examples of transcendental Julia sets with non-extreme packing dimensions and shows these dimensions are dense in (1,2).

## Key findings

- Julia sets with packing dimension in (1,2) constructed.
- Packing dimensions are dense in the interval (1,2).
- Hausdorff dimension can be arbitrarily close to packing dimension.

## Abstract

We construct a family of transcendental entire functions whose Julia sets have packing dimension in $(1,2)$. These are the first examples where the computed packing dimension is not $1$ or $2$. Our construction will allow us further show that the set of packing dimensions attained is dense in the interval $(1,2)$, and that the Hausdorff dimension of the Julia sets can be made arbitrarily close to the corresponding packing dimension.