We ❤️ PDEs

Here are some examples of a PDE solutions on a domain based on a heart-shaped curve.

Excitability

Models like FitzHugh–Nagumo are the basis for a lot of work in cardiac electrophysiology and related areas. So let’s solve these PDEs in a heart!

• Load the interactive simulation and enjoy. You can click and select 3D to get a 3D view of the beating heart. Try this simulation for a crude implementation of these equations on a growing domain.

Chemotaxis

The next example is based on the Keller–Segel model for chemotaxis. Load the interactive simulation and enjoy! Try this simulation for a crude implementation of these equations on a growing domain.

Warm hearted

By plotting vector fields on top of the solutions to PDEs, as exemplified in the heat equation, we can visualise how heat flows from a source as it traces out a heart in this interactive simulation.