# Growing Perfect Decagonal Quasicrystals by Local Rules

## TL;DR

This paper introduces a 3D local growth algorithm for creating perfect decagonal quasicrystals, enabling the assembly of defect-free structures layer by layer, challenging the need for non-local information in quasicrystal formation.

## Contribution

It presents a novel local growth rule in 3D that allows for the formation of perfect decagonal quasicrystals from a Penrose tiling, demonstrating a purely local construction process.

## Key findings

- Successful growth of perfect Penrose tiling layers on decapod tilings
- Formation of defect-free decagonal quasicrystals in bulk
- Contradicts the belief that non-local information is necessary for 2D PPT growth

## Abstract

A local growth algorithm for a decagonal quasicrystal is presented. We show that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to form on the upper layer, successive 2D PPT layers can be added on top resulting in a perfect decagonal quasicrystalline structure in bulk with a point defect only on the bottom surface layer. Our growth rule shows that an ideal quasicrystal structure can be constructed by a local growth algorithm in 3D, contrary to the necessity of non-local information for a 2D PPT growth.