Where chaos shows up
Applications
Chaos theory is not just mathematics. It shows up in weather forecasting limits, secure communication, neuron firing, population biology, lasers, and more.
Cryptography
Chaotic maps as primitives for ciphers, hash functions, S-box generation, image encryption, and PRNGs.
Weather & climate
Lorenz's 'butterfly effect': why deterministic atmospheric models hit a 2-week predictability horizon.
Biology & physiology
Population dynamics, cardiac arrhythmia, EEG and neural firing, epidemics, immune dynamics.
Economics & finance
Chaotic models of business cycles, exchange-rate dynamics, the long debate over chaos in markets.
Electronic circuits
Chua's circuit, Colpitts, memristive chaos, chaos-based secure communication.
Optics & lasers
Ikeda ring cavity, Lorenz-Haken laser equations, optical chaos for random number generation.
Control & synchronisation
OGY, Pyragas, Pecora-Carroll synchronisation, master stability function, chaos shift keying.
Reservoir computing & AI
Echo-state networks, liquid-state machines, chaotic optimisation, edge-of-chaos computation.
Art & sonification
Strange attractor visualisation, attractor sonification, generative chaotic music.