Pattern formation · Hyperuniformity · Emergent order

Geometry-driven complexity

How can simple geometric interactions generate large-scale order?

Overview

This research theme traces my entry into complexity science through geometry-driven hyperuniformity and related questions of pattern formation. It asks how local geometric interactions, constraints, and relaxation rules can generate large-scale order.

Interactive demo

The interactive Lloyd demo provides an intuition-building way to explore how local relaxation dynamics can transform point configurations and their emergent structure.

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Relevant publications

This list is intended for publications connected to geometry-driven hyperuniformity, pattern formation, local relaxation, and emergent order.

Scale-free correlations in two-dimensional geometry-driven hyperuniformity

Authors: Sungyeon Hong, Mohammad Saadatfar
Year: 2025
Publisher: Data-Driven Modelling: Unravelling Complexity in the Sea of Data

This work investigates how large-scale order can emerge from simple local interactions. Using a computational process known as Lloyd's algorithm, we show that a disordered collection of points can self-organise into a hyperuniform state characterised by orientational domains whose sizes grow with the system itself. The absence of a characteristic length scale suggests a form of scale-free organisation, a hallmark of systems capable of coordinated collective responses across many scales.

Topological mechanical states in geometry-driven hyperuniform materials

Authors: Sungyeon Hong, Can Nerse, Sebastian Oberst, Mohammad Saadatfar
Year: 2024
Publisher: PNAS Nexus

Can disorder be engineered to produce useful physical behaviour? In this study, we reveal how topological defects that emerge during the formation of hyperuniform structures give rise to distinct mechanical states capable of localising vibrational energy. By connecting geometry, topology, and mechanics, this work demonstrates how robust functional properties can arise from self-organising disordered materials.

Dynamical arrest of topological defects in 2D hyperuniform disk packings

Authors: Sungyeon Hong, Michael A. Klatt, Gerd Schröder-Turk, Nicolas François, and Mohammad Saadatfar
Year: 2021
Conference: Powders & Grains 2021 – 9th International Conference on Micromechanics on Granular Media

This paper explores how topological defects evolve during the formation of hyperuniform structures. We show that as the system becomes increasingly ordered, defects slow down and eventually become trapped, leaving a characteristic structural signature. The results provide insight into how local topological processes shape the emergence of large-scale order in complex systems.