I am two days of work on my jam project &delta-xy-plotter

I've got the particle system tuned to do a pretty good job accentuating the flow of the differential equation that is being plotted. It has rules for randomly spawning in new particles when possible, killing particles that are too close to standing still, and killing particles in areas that are too dense. This seems to create a nice balance of covering the plot in particles without making the density so high you can't actually "read" the plot at all.

In this animation I am using the classic Lotka-Volterra equations for modelling predator-prey interactions, and I am changing the base growth rates for each species over time to see the plot changing.