VisualPDE is a website designed to bring the world of partial differential equations (PDEs) to a wider audience through the use of real-time interactive web-based simulations, usable on almost any device.

This heart-shaped pattern isn’t a video. It’s a simulation of a PDE system running live on your device. We provide numerous example simulations on the site, exploring a wide variety of topics from waves and transport theory, to chaotic nonlinear physical systems and pattern-forming models in mathematical biology. VisualPDE simulations can also be found in recent scientific works (see below), allowing you to instantly reproduce cutting-edge findings live on your device.

People using VisualPDE

Tens of thousands of simulations have been performed using VisualPDE. External applications of VisualPDE include:

Using VisualPDE

Our collections of Visual Stories and Introductory PDEs are a good place to start exploring, after which you can delve into the other collections found on the home page. You can also check out our detailed User guide and the dedicated Quick start guide.

Beyond our curated examples, we hope to encourage advanced users to design their own simulations. Anyone can design their own model simulations and share them with a URL, or copy the markdown-based website from GitHub to design their own website for use in teaching or research communication (see our licence if you’re looking for industrial use).

Origins and contributors

The ideas for this website originated in a Durham Centre for Academic Development collaborative innovation grant titled Accessible interactive visualisations in mathematical biology, which supported Alex Chudasama (a final-year undergraduate at Durham University) to design an early version of an interactive PDE solver based on this Gray–Scott reaction–diffusion simulator.

The current website and tools are written and maintained by Benjamin Walker, Adam Townsend and Andrew Krause. A detailed article about the context, design, and applications of VisualPDE can be found in the Bulletin of Mathematical Biology.