Simulating waves, chaos and synchronization with a microcontroller.

The spatiotemporal dynamics of complex systems have been studied traditionally and visualized numerically using high-end computers. However, due to advances in microcontrollers, it is now possible to run what once were considered large-scale simulations using a very small and inexpensive single integrated circuit that can furthermore send and receive information to and from the outside world in real time. In this paper, we show how microcontrollers can be used to perform simulations of nonlinear ordinary differential equations with spatial coupling and to visualize their dynamics using arrays of light-emitting diodes and/or touchscreens. We demonstrate these abilities using three different models: two reaction-diffusion models (one neural and one cardiac) and a generic model of network oscillators. These models are commonly used to simulate various phenomena in biophysical systems, including bifurcations, waves, chaos, and synchronization. We also demonstrate how simple it is to integrate real-time user interaction with the simulations by showing examples with a light sensor, touchscreen, and web browser.