five small worlds · five animated equations
Things I render to remember they're real.
Each of these is a live simulation, not a video. Drag the sliders; the math reacts. Each page has the equation, the physical story, and the moment it broke my brain the first time I met it.
Higgs collision
CMS event display at √s = 13 TeV. Charged particles spiraling in a 3.8 T solenoid. The 125 GeV excess that took 50 years and 10,000 people to find.
dx/dt = σ(y−x)Lorenz attractor
Three ordinary differential equations. Nothing hidden, nothing random, nothing quantum. And, in practice, completely unforecastable. The first chaos.
φ = (1+√5)/2Golden spiral
A logarithmic spiral with a famous growth factor. The math is real; the "nature loves φ" claim is mostly post-hoc pattern matching. But plants and shadows, yes.
V = π · A → ∞Gabriel's horn
Finite volume. Infinite surface area. You can fill it with paint but you cannot paint the inside of it. The first time most students realize "infinite" comes in different sizes.
x = sin(at+δ), y = sin(bt)Lissajous figure
Two perpendicular sine waves. Closed when the frequency ratio is rational. Phase drift turns the math into a movie. Pre-digital oscilloscopes used these to tune signals by eye.
Next up
Two simulations I want to build next. Neither is simple. Both are worth doing.
Black hole simulation. Runge-Kutta numerical integration of the relativistic geodesic equations. Photon paths bending around a Schwarzschild black hole, rendered in real time. The goal is to show the photon sphere — the radius at which light orbits — and the shadow.
N-body galaxy simulation. Gravitational simulation of galaxy formation. Start with a disk of mass, perturb it, watch spiral arms emerge from gravity alone. The interesting part is not the simulation — it's the numerical stability over long timescales.