Lorenz Attractor (Chaos Theory)

A system of ordinary differential equations noted for having chaotic solutions. It famously demonstrates the "butterfly effect" where tiny differences in initial conditions yield diverging outcomes.
dx/dt = σ(y - x)
dy/dt = x(ρ - z) - y
dz/dt = xy - βz
This ASCII version projects the 3D trajectory onto a 2D text grid. Add a tracer to inject a new particle with a microscopic difference in its starting position, and watch its path eventually diverge completely from the original.