1. Capacity Dimension of The Hénon Attractor
Eui-Sun Lee
Department of Physics
Kangwon National University
 Hénon Map
 Chaotic Attractor with A Positive Lyapunov Exponent (0.367) for b=0.3 and A=2.1.

2. Geometrical Structure of The Hénon Attractor
1st close-up
2nd close-up
Successive Magnification  Self-Similar Structure on All Scales
 Hénon Attractor: Strange Attractor with Fractal Structure

3. Capacity Dimension  Definition
To characterize a strange attractor, let’s cover it with boxes of length  .
As the length  is decreased, the number of boxes N( ) obeys a power-law scaling.
In the limit  0, the exponent characterizing the strangeness of the attractor,
is called the Capacity Dimension.

4.  Plot of log10 N() vs. log10  -1 for the Hénon Attractor
The slope of the graph gives the capacity dimension D0(=1.2690.009)
of the Hénon attractor.

5. Summary
The Hénon attractor is a strange attractor with the capacity dimension D0(=1.2690.009).
Since 1 D0  2, it has a fractal geometry that is intermediate between a line and a plane.