# Growth Forms of Tilings

## TL;DR

This paper reviews the concept of growth forms in tilings, discussing current results, conjectures, and open questions across various tiling types such as periodic, multigrid, substitution, and hat tilings.

## Contribution

It provides a comprehensive overview of the state of research on growth forms of tilings, highlighting key results and open problems.

## Key findings

- Summarizes known results on growth forms of different tiling types.
- Identifies open questions and conjectures in the study of tiling growth forms.
- Discusses the diversity of growth behaviors in various tiling classes.

## Abstract

The growth form (or corona limit) of a tiling is the limit form of its coordination shells, i.e. its set of tiles located at a fixed distance from some tile. We give an overview of current results, conjectures and open questions about growth forms, including periodic, multigrid, substitution, and hat tilings.