Strange Attractors
Explore fourteen continuous flows, regular comparisons and true delay dynamics with current states, projections and model-specific quantities.
About this tool
Compare regular and irregular flows
Select a model and view, then Run. The finite preparation first computes the warm-up and an initial visible trace; Cancel stops it. Pause, One step and PNG inspect the resulting state. One step always advances one model step. Inputs invalidate the old experiment; changing view starts a new run from the same selected initial state. Fit view restores the 3D camera. Drag rotates; Ctrl/Meta-wheel zooms, plain wheel scrolls.
Read the models honestly
Not every preset is a strange attractor, and varying coefficients can produce regular motion, equilibrium or escape. Lotka–Volterra and autonomous van der Pol are regular comparison models. Piecewise feedback and damped feedback retain their explicitly defined toy equations without a claim of multi-/double-scroll chaos. Sprott uses the author’s dissipative case B: ẋ=yz, ẏ=x−y, ż=1−xy. Lorenz defaults to σ=10,ρ=28,β=8/3. Number fields retain precision and accept decimal comma and parameter fractions.
Delay and quantities
Mackey–Glass: ẋ=βx(t−τ)/(1+x(t−τ)^n)−γx(t), default τ=17 and constant past history x=1.2. RK4 uses the method of steps and linear interpolation of stored past values. The displayed three coordinates are a delay embedding, not three ODE states. The perturbed trajectory shifts the whole constant history by ε. Initial values must be nonnegative.
Hénon–Heiles H=(pₓ²+pᵧ²+x²+y²)/2+λ(x²y−y³/3). The quantity plot shows ΔH from each own initial value. Lotka–Volterra shows drift of I=δx−γlnx+βy−αlny for positive populations. Duffing E=v²/2+αx²/2+βx⁴/4 and van der Pol E=(x²+v²)/2 are mechanical diagnostics, not conserved for driven/dissipative motion. Unsupported energy views are not offered.
Sections and numerical scope
For higher-dimensional flows, choose the plane normal/value; displayed axes exclude the normal. Positive crossings use linear interpolation within the time step. Driven Duffing uses a stroboscopic sample once per forcing period. Autonomous planar flows have no misleading empty section option. Time series compare both starts on a shared scale and actual model-time axis.
Model times and states are dimensionless. Integration uses each model’s RK4 step multiplied by the selected factor; reduce that factor to assess error. Delay interpolation limits global accuracy. Nearby-state distance is not a Lyapunov certificate and a finite trace cannot prove chaos. Playback uses fixed steps and can slow under load; hidden tools suspend it. The configured retained trace is capped only by the selected sample limit, not screen pixels. Numerical-range escape stops the run. PNG pauses and captures current pixels and reproduction parameters. 3D needs WebGL.