Physics of Chaos
A simulation to show the butterfly effect from a lorenz attractor
What it does
The fact that a fixed set of equations (with deterministic variables) do not result in a predictable long term pattern is the cool math part. The path traced by the solution of the differential equations also produce a nice butterfly like pattern known as the Lorenz Attractor.
Edward Lorenz developed the system as a simplified mathematical model for atmospheric convection. He was attempting to model the way air moves when heated from below and cooled from above.
A neat optimization is that the simulation only uses Tiachi for the particle path calculations but the actual rendering is done using PyGame to ensure a smooth 60 FPS even on machines without a discrete GPU. The optimization trick suggested by Claude code from my first sim build and I carried over that idea to my submission as well.