Systems, Signals & Computation
An interactive field guide to how things change, oscillate, propagate, and compute — from a swinging pendulum to chaos, waves, networks, and learning machines.
Systems, Signals & Computation
An interactive field guide to the mathematics of change and pattern. It starts with dynamical systems — anything whose state evolves by a fixed rule, like a swinging Pendulum — and follows the threads outward: into the oscillations and Waves that motion makes, the Fourier Analysis that decomposes any signal, the Chaos that simple rules can hide, and the networks, randomness, information, and optimization that turn dynamics into computation. Almost every page has a live simulation you can poke.
Ways in
Foundations — the language of the field: State Space, Phase Portrait, Fixed Point, Stability, Attractor, and the Lyapunov Exponent that measures chaos.
Oscillations — things that repeat: the Simple Harmonic Oscillator, the Pendulum, Resonance, and self-sustaining Limit Cycles.
Waves — oscillation set loose in space: the Wave Equation, Standing Waves, Interference, Beats, and the Doppler Effect.
Fourier Analysis — every signal as a sum of sinusoids: Fourier Series, the Fourier Transform, Harmonics, and the Uncertainty Principle.
Chaos — deterministic yet unpredictable: the Lorenz System, the Double Pendulum, the Logistic Map, and Strange Attractors.
Complex Systems — many simple parts, emergent wholes: the N-Body Problem, Conway's Game of Life, Predator–Prey Dynamics, and Reaction–Diffusion patterns.
Linear Algebra — the math under all of it: Vectors, matrices as Linear Transformations, and the Eigenvalues and Eigenvectors that decide Stability and rank the web.
Graph Theory & Networks — nodes and edges everywhere: Breadth-First Search, Dijkstra's Algorithm, PageRank, and Small-World Networks.
Probability & Random Processes — structure in randomness: the Random Walk, the Central Limit Theorem, Markov Chains, and Brownian Motion.
Information Theory — measuring surprise and its limits: Entropy, Huffman Coding, Error-Correcting Codes, and Channel Capacity.
Optimization & Learning — searching a landscape for the best point: Gradient Descent, Simulated Annealing, the Perceptron, and Neural Networks.
Cryptography — keeping secrets and proving identity: the Caesar Cipher, the unbreakable One-Time Pad, Diffie–Hellman key exchange, RSA, and Digital Signatures.
Number Theory — the integers and their secrets: Prime Numbers, the Sieve of Eratosthenes, the Euclidean algorithm, and the Ulam Spiral.
Computability & Complexity — the limits of computation: the Turing Machine, the Halting Problem, Big-O Notation, and P versus NP.
A taste of the whole field in one picture
Below, the same rule runs from many slightly different starting points. They track together, then diverge — the essence of Sensitive Dependence on Initial Conditions.
Start with the Foundations, or jump straight into the Lorenz System.