Catching Lightning in an IMU

Simulating Diffusion-Limited Aggregation with a Raspberry PI RP2040 MCU

- Angela Cui, Nathaniel Navarro, William Yoon

A bolt of lightning flashes across the sky and scientists marvel at diffusionlimited aggregation, a process in which random moving particles join to form static clusters. Three Cornell University students, Angela, Nathaniel and William, use an RP2040 and an inertial measurement unit to build a cyclic DLA simulator to tap into technology's ability to shed insight on natural processes like the formation of lightning.

The formation of snowflakes, the growth of crystals, and the path taken by lightning are all examples of natural phenomena can be modeled by diffusion limited aggregation (DLA), the process by which particles undergo a random walk and cluster together. Inspired by technology's ability to help us better understand natural processes, we built an interactive, diffusion-limited aggregation simulator as our final project for Cornell University's Digital System Design using Microcontrollers class. We augmented with motion controls that enabled users to manipulate the behavior of our simulated particles.

What Is DLA? Diffusion-limited aggregation models systems in which particle transport occurs primarily through diffusion, and particles tend to cluster around a pre-existing aggregate. DLA can model systems such as dielectric discharge, mineral aggregation, and even snowflake formation, an example of which is shown on a frosty window in Figure 1.

DLA models diffusion by simulating Brownian motion of particles. In a given time step, particles move by an amount sampled from a random normal distribution. The equation for the probability distribution of a normal distribution is shown below, where depends on the time step and simulation parameters. The 0 in the exponent expresses the notion that a particle is equally likely to go in one direction as it is the other.