Education

Interactive articles and simulations.

Explorations of physics, computation, and intelligence. Each article includes interactive demonstrations.

Foundations

Toolkit
Physics Toolkit: A Guided Tour
Vectors, dot products, linear maps, eigenvectors, damped oscillators, and Fourier.
Interactive
Primer
Physics & Math Primer
Complex phase, rotations, spacetime metric, two-state systems, potentials, and gauge ideas.
Interactive
Math
Graph Theory: A Practical Guide
Paths and cuts, trees and flows, spectra and diffusion.
Article
Theory
Spacetime, Fields, and Light
Lorentz boosts, spin-1/2, gauge symmetry, Higgs, neutrino oscillations, gravitational lensing.
Interactive

Agents & 3D Motion

Article
How Flies Move in 3D
3D motion on SE(3): rotations, translations, proposals, on-manifold updates.
Article
Simulation
3D Flies Simulator
Add goals, hazards, and plumes. Watch motion respond in real time.
Simulator

Shapes & Patterns

Interactive
Shapes, Paths, and Patterns
Hands-on visuals for symmetry, shapes, and motion.
Interactive

Computation & Automata

Computation
NFAs from First Principles
Nondeterminism, epsilon-moves, and subset construction with a live runner.
Interactive
Computation
Turing Machines & Automata
Run a DFA for parity and a Turing machine that edits tape step by step.
Interactive

Neural Networks & Transformers

AI
Neural Networks & Transformers
Linear units, loss, gradient, softmax, attention, positional encodings, layer norm.
Interactive

Playground

Simulation
Game of Flies
Place houses and hazards. Flies join teams, orbit flags, and switch sides.
Sandbox