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For K-12 Students · Strange Attractors

Strange Attractors for a mass on a spring

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a mass on a spring live below — adjust the inputs and watch it respond, right in your browser.

Strange Attractor GalleryLive

3D chaos · drag to orbit

Controls

Five famous strange attractors in 3D. Tune the Lorenz constants, then drag to orbit around the chaos.

Presets

σ (sigma)

ρ (rho)

β (beta)

Integration points

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Data Inspector

AttractorLorenz

Points19,799

ρ (rho)28

TypeStrange / chaotic

Governing equation

\overset{x}{˙} \overset{y}{˙} \overset{z}{˙} = σ (y - x) = 10 (y - x) = x (ρ - z) - y = x (28 - z) - y = x y - β z = x y - 2.667 z

Reading this result: Classic Lorenz (ρ=28, σ=10): the trajectory orbits two lobes forever without ever repeating. Sensitive dependence on initial conditions means the tiniest nudge changes everything — the butterfly effect.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Strange Attractors for a mass on a spring" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.