Chaos Lab
Tools
Interactive playgrounds. Everything runs locally in your browser; nothing is sent to a server.
1D maps
Logistic playground
Iterate r·x·(1−x), see cobweb + time series + Lyapunov live.
Cobweb plot
Generic cobweb for logistic, tent, sine, Bernoulli, Gauss, Chebyshev, PWLCM.
Bifurcation studio
Logistic, sine, tent, cubic, Gauss: scrub the parameter range.
Lyapunov vs parameter
Numerical λ(r) chart for any 1D map.
2D maps
Hénon explorer
Drag through (a, b) parameter space to scan the Hénon family.
Arnold cat map
Apply Arnold's hyperbolic toral automorphism. Watch Poincaré recurrence.
Ikeda explorer
Optical ring-cavity strange attractor; tune u.
Tinkerbell explorer
Four-parameter 2D map with a dragon-shaped attractor.
Standard map
Chirikov's twist map; Poincaré section with multi-colour trajectories.
Flows
Lorenz attractor
Drag to rotate, scrub σ/ρ/β, see the butterfly emerge.
Rössler attractor
Single-scroll attractor, a/b/c sliders.
Chen system
Generalised-Lorenz double scroll.
Lü system
Bridges Lorenz and Chen topologically.
Chua's circuit
Double-scroll attractor with piecewise-linear Chua diode.
Duffing oscillator
Driven, damped double-well; period-doubling to chaos.
Van der Pol
Self-sustained relaxation oscillator; mode locking + chaos when forced.
Double pendulum
Two pendulums, ε = 10⁻⁴ apart, diverge in seconds.
Mackey-Glass
Delay-differential equation with delay embedding visual.
Hindmarsh-Rose neuron
3-variable neuron model with chaotic bursting.
Sprott gallery (A-S)
19 minimal-chaos flows, click to swap.
Spatial
Analysis
Recurrence plot
Compare periodic, chaotic, stochastic, and delay-system time series.
Power spectrum
Fourier signature: discrete spikes vs broadband chaos.
0-1 test for chaos
Gottwald-Melbourne binary test on any scalar time series.
Lyapunov from CSV
Rosenstein algorithm on uploaded time series or built-in samples.
Box-counting dimension
Estimate D₀ from Hénon, Ikeda, Sierpinski, Lorenz Poincaré section.
Control & sync
Symbolic
Computation
Reference
Bifurcation atlas
Six codim-1 bifurcations: normal form + (μ, x*) diagram.
NIST randomness suite
8 NIST SP800-22 tests on chaotic PRNGs vs Math.random and a biased baseline.
Chaos-based PRNG
Generate, visualise (histogram + lag plot), and download bytes from logistic / tent / PWLCM / Chebyshev / Hénon.
Chaos image cipher
Upload an image, encrypt with a chaotic map keystream + pixel permutation, re-upload with the same key to decrypt.