Shapes of polynomial Julia sets, revisited

TL;DR

This paper demonstrates that any finite union of disjoint Jordan curves in the complex plane can be approximated arbitrarily closely by polynomial Julia sets, with a constructive proof provided.

Contribution

It provides a constructive method to approximate arbitrary finite unions of Jordan curves using polynomial Julia sets.

Findings

Finite unions of Jordan curves can be approximated by polynomial Julia sets

The approximation is arbitrarily close in the Hausdorff topology

The proof of approximation is constructive

Abstract

Any finite union of disjoint, mutually exterior Jordan curves in the complex plane can be approximated arbitrarily well in the Hausdorff topology by polynomial Julia sets. Furthermore, the proof is constructive.