The Hénon Attractor - A Strange Attractor in 2D

Click and drag to zoom. Double-click to reset.

Parameter a: 1.4

Parameter b: 0.3

Iterations: 100,000

X range [-1.5, 1.5]

Y range [-0.5, 0.5]

Zoom level 1×

Points plotted —

The Hénon Map

x_n+1 = 1 - a·x_n² + y_n

y_n+1 = b·x_n

🔬 Fractal Structure

Zoom into any "line" and discover
it's made of parallel lines...
which are made of more lines...
Dimension ≈ 1.26

🌀 What Is It?

The Hénon attractor is a strange attractor—a set that chaotic trajectories approach and never leave. It's "strange" because it has fractal structure: not a smooth curve, not a scattered dust, but something in between with dimension 1.26.

📏 Cantor Meets Line

Slice through the attractor and you find a Cantor set! What looks like a single curve is actually infinitely many parallel curves. Zoom in and each "line" splits into more lines. It's smooth in one direction, a Cantor dust in the perpendicular direction.

🔄 Stretch and Fold

The map stretches the plane (creating chaos) while folding it back (keeping trajectories bounded). This stretch-and-fold action, repeated infinitely, creates the intricate layered structure. It's like kneading dough forever.

🪐 Hénon's Goal

Michel Hénon created this in 1976 as a simplified Lorenz system. The Lorenz attractor lives in 3D continuous time; Hénon captured similar chaos in 2D discrete time. Astronomers still use it to model stellar orbits in galaxies!