Interactive articles and demos on physics, computation, and intelligence.
Foundations
Build the basics, then see them in action with live physics visuals.
Path: Primer → Core ideas
Toolkit
Physics Toolkit: A Guided Tour
Vectors and dot product, linear maps and eigenvectors, basis mixing, damped oscillators, and a small Fourier builder.
Primer
Physics & Math Primer: A Practical Introduction
Interactive primer for complex phase, rotations, spacetime metric, two‑state systems, potentials, and basic gauge ideas.
Math
Graph Theory: A Practical Guide
Paths and cuts, trees and flows, spectra and diffusion: graphs as a universal language for networks.
Theory
Spacetime, Fields, and Light
Interactive visuals and equations for Lorentz boosts, spin‑1/2, gauge symmetry, the Higgs mechanism, neutrino oscillations, and gravitational lensing.
Agents and 3D Motion
Read the idea, then explore the simulator that implements it.
Path: Article → Simulator
Article
How Flies Move in 3D
3D motion on SE(3): rotations + translations, proposals, and on‑manifold updates.
Simulation
3D Flies Simulator
Click to add goals, hazards, and plumes. See how motion responds in real time.
Shapes and Patterns
Interact with symmetry and topology‑inspired visuals.
Interactive
Shapes, Paths, and Patterns
Hands‑on pictures that make symmetry, shapes, and motion easy to see and understand.
Computation & Automata
Small machines that recognize patterns and run algorithms.
Path: DFA → Turing machine
Computation
NFAs from First Principles: Interactive
Nondeterminism, ε‑moves, and subset construction with a live runner and builder.
Computation
Turing Machines & Automata: Interactive
Run a DFA for parity and a Turing machine that edits a tape step by step; see the formal parts in action.
Neural Networks & Transformers
Core ideas behind modern deep learning, made visual.
AI
Neural Networks & Transformers: A Visual Introduction
Linear units, loss & gradient, softmax, attention, positional encodings, layer norm, residuals, receptive fields.
Playground
Open‑ended sandbox to try ideas quickly.
Simulation
Game of Flies
Place houses and hazards. Flies join teams, orbit flags, and sometimes switch sides.