Strange Attractor Gallery

Render Rossler, Henon, Duffing, and other strange attractors. Adjust parameters and watch phase portraits morph in real time.

Tested tool guide Tested browser tools Checked August 16, 2026

What Strange Attractor Gallery does, with a checked example

This gallery renders phase portraits of the classic strange-attractor systems: the Rossler flow, the forced Duffing oscillator, and the Henon map, plus variants of each. Every system exposes its defining parameters on sliders, and the plot redraws as you move them, so you can watch an orbit fold into a chaotic band or collapse back onto a plain loop. The thing most visitors get wrong: the famous chaotic pictures are fragile. Most parameter values produce a dull fixed point or a simple periodic orbit; the iconic chaos lives in narrow ranges such as Henon's a = 1.4 or Rossler's c = 5.7.

Worked example

A concrete input and expected output from the current implementation.

Input

Henon map, a = 1.4, b = 0.3

Expected output

A phase portrait in the x-y plane: thousands of discrete points packed into a thin, folded, banana-shaped band. The orbit opens with scattered transient points (from the origin: (1.0, 0.0), (-0.4, 0.3), (1.076, -0.12), (-0.741, 0.3228)) before settling onto the band, which fills in further as more points are drawn.

With a = 1.4 and b = 0.3 the Henon map is dissipative and chaotic, so every starting point in its basin is pulled onto the same thin band, which is what any run with these parameters shows. The iterates follow from x(n+1) = 1 - 1.4 x(n)^2 + y(n), y(n+1) = 0.3 x(n): (0, 0) -> (1.0, 0.0) -> (-0.4, 0.3) -> (1.076, -0.12) -> (-0.741, 0.3228).

How the result is produced

Continuous flows and discrete maps

The systems come in two kinds. Rossler and Duffing are continuous: their equations are stepped forward in time to trace a single long orbit, and the plot shows that orbit's projection onto the phase plane. Henon and the other maps are iterated instead: each plotted point is the previous point pushed through the map, with no connecting curve. Either way the evolution is deterministic, so the same parameters and initial condition always draw the same picture.

Abrupt changes at bifurcations

An attractor's shape can change discontinuously with the parameters. As a slider crosses a bifurcation value, the orbit switches type - fixed point to loop, loop to doubled loop, then to chaos - so one small drag can replace the entire picture. Each slider position shows the fully developed orbit for that exact setting, which is why the motion you see is a jump between regimes rather than a gradual deformation.

Good uses

Verifying a textbook figure: enter the printed parameter values - say Rossler's a = 0.2, b = 0.2, c = 5.7 - and compare the rendered portrait with the book's illustration of the single-lobed chaotic attractor.
Classroom demonstrations of chaos: sweep a parameter such as Rossler's c or Henon's a and show the orbit period-doubling into chaos, then sliding back into periodic motion as the parameter returns.
Hunting for striking shapes for illustrations or generative art: many parameter combinations yield folded or symmetric forms, and the live redraw makes it easy to sample candidates quickly.

Limits and checks

One orbit, not the whole attractor: the plot is a single trajectory from one initial condition. With only a few plotted points, the starting transient dominates the picture; let it run so the orbit settles, and know that a different starting point draws a different point sequence that lands on the same shape.
A blank canvas usually means escape: for many settings the orbit diverges to infinity - Henon with a above roughly 1.43, Rossler in parts of its parameter space. An empty plot is the correct result for those parameters, not a bug; pull the slider back toward the known chaotic values.
A phase portrait carries no timing: it shows state, not time. A closed loop tells you the motion is periodic but not its period or frequency, and a chaotic band does not reveal how fast the orbit travels through it.

Common questions

Same parameters as a book, but my plot looks different - did I enter something wrong?

Probably not. The attractor's shape is fixed by the parameters alone, but the visible point cloud depends on the starting value and on how many points have been drawn. The early transient differs, and in chaos no two trajectories ever repeat a point. Let the plot run and it fills in the same band the book shows.

Can I reproduce an exact sequence of points, say for a data table?

For chaotic parameters, no. Even a tiny difference in the starting value or in rounding produces a completely different itinerary, and this tool draws pictures; the raw iterates are not part of its output. The shape is reproducible; the individual points are not. Under periodic parameters the orbit repeats exactly and is fully reproducible.

References and verification

The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.

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