Hénon Map - A Discrete Strange Attractor

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Controls

Parameters

a (stretching) 1.4

b (contraction) 0.3

Presets

Statistics

Points plotted 0

Fractal dimension ~1.26

Lyapunov exponent ~0.42

Fixed Points

Saddle (0.631, 0.189)

Repeller (-1.131, -0.339)

The Equations

x_n+1 = 1 - ax_n² + y_n
y_n+1 = bx_n

Introduced by Michel Hénon (1976) as a simplified model for the Poincaré section of the Lorenz system. These two equations generate infinite complexity.

Strange Attractor

For a=1.4, b=0.3, points neither escape to infinity nor settle to a fixed point. Instead, they trace out a FRACTAL structure—smooth in one direction, a Cantor set in another. Zoom in and the detail is infinite!

Stretch and Fold

Parameter 'a' controls stretching (chaotic mixing), 'b' controls folding (contraction). The attractor emerges from this eternal dance: stretch, fold, stretch, fold—creating layered structure without self-intersections.

Basin of Attraction

Not all starting points reach the attractor! Some escape to infinity. The boundary between these regions is itself a fractal—infinitely complex, sensitive to the tiniest perturbation. Switch to "Basin" mode to see this.

The Hénon Map