Below is a collection of pretty math images that I’ve created.
I was trying to simulate the Poisson process but screwed it up. The picture should look like a jagged, ascending staircase, but I forgot to sum the results up, giving what looks like the skyline of a blocky city. I thought this was cooler than whatever I was trying to do, so I played with my mistake instead.
Someday I would like to make an endless animation of this.
This plot shows the difference between the “classical” Lotka–Volterra equations and a stochastic version of them which adds some randomness. In the classical version, predator and prey populations enter a stable equilibrium (the oval-looking thing) and never leave it. The stochastic version lets you jump around more, and looks much more interesting.