Voronoi Growth: 2D Crystallisation

What is Voronoi Growth?

Voronoi growth refers to the process where regions are divided based on proximity to points in space, creating intricate patterns. In 2D crystallisation, this concept is applied to simulate how grains grow and interact with each other.

The simulation starts by placing seeds randomly or according to a specific nucleation mode, then grows these seeds into larger areas (grains) while respecting the chosen distance metric.

How Does Voronoi Growth Work?

Grain growth in this context is driven by the minimisation of surface energy. As grains grow, they expand to cover more area, and their boundaries adjust based on the proximity to other seeds or grains.

The Lloyd relaxation step refines the positions of the seeds to ensure a more uniform distribution across the space, which can lead to more complex and aesthetically pleasing patterns.

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Why Does It Matter?

Understanding Voronoi growth is crucial in materials science for predicting how metals and other crystalline materials form during cooling processes.

In computer graphics and generative art, it provides a method to create realistic textures and patterns that mimic natural phenomena.

Real-World Applications

Voronoi diagrams are used in urban planning to optimise the distribution of resources like public services or infrastructure.

In biology, they can model cell growth and tissue formation processes.

Frequently asked questions

What is Lloyd relaxation?

Lloyd relaxation involves iteratively moving each seed to the centroid of its Voronoi cell, which helps in achieving a more uniform distribution of seeds and smoother grain boundaries.

How does changing the distance metric affect the simulation?

Different distance metrics (e.g., Euclidean, Manhattan) can significantly alter the shape and size of grains, leading to diverse patterns that reflect different physical conditions or growth scenarios.

What is nucleation in this context?

Nucleation refers to the initial formation of a new phase within a material. In the simulation, it determines how seeds are initially placed on the canvas, which can influence the overall pattern and grain structure.

Why use Voronoi diagrams for generative art?

Voronoi diagrams offer a natural way to create complex patterns that mimic real-world phenomena, providing artists with a powerful tool to generate aesthetically pleasing and mathematically interesting designs.

Try it live

Everything above runs in your browser — open Voronoi Growth: 2D Crystallisation and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Voronoi Growth: 2D Crystallisation simulation