In 1993 I took a graduate seminar in Chaos Theory that was fascinating. We studied a wide variety of systems, like Cellular Automata, The Game of Life, and Mandlebrot Sets. We also studied non-linear dynamic systems. One that I did a deep dive on was modeling a car chained to the top of a flat-bed trailer as it went down the road. Another one that we studied was the logistic model, or the Lotka-Volterra predator-prey model.
The Predator/Prey logistic model wasn't particularly CPU intense but it was interesting because slight perterbations in the model can cause drastic changes in equilibrium - or extinction! I've created a model that lets you alter the system parameters so you can see what happens to the ecosystem.