Here are some basic notions for understanding this program and the above screenshots:
1. The Jacobian matrix
of the dissipative Hénon map
is given by
2. Therefore the determinant of the Jacobian matrix is
, the Hénon map is area-contracting; for
, area-preserving; and for
, area-expanding. (See the screenshots 5–7.)
, something interesting happens because it is the conservative limit of the dissipative Hénon map. By solving fixed point equations of the first and the second iterated Hénon map with
, it is easy to find that there are two types of solutions, two hyperbolic solutions
with period 1 (THS) and two elliptic solutions
with period 2 (TES). For
, the THS is approximately
, while the TES is approximately
, as shown in the fourth screenshot.
5. By carefully locating the points on the initial circle to pass through one of the TES (i.e. either
) you can see two beautiful yin-yang-like spirals (one is located at the top-left and the other at the bottom-right), which are shown in the first screenshot . Here the radius
of the initial circle is given by
. Since this is the conservative limit of the dissipative Hénon map, these yin-yang-like spirals near the TES can exist forever without contracting or expanding.
6. The shape and the color of these spirals become very close to those of the true yin-yang spiral by imagining that the initial circle is filled in with black dots .
7. This numerical experiment may give us some hints about why Jupiter's red spot and Saturn's hexagon-shaped hurricane seem to exist forever without contracting or expanding [6–7].
 M. Hénon, "A Two-Dimensional Mapping with a Strange Attractor," Communications in Mathematical Physics
(1), 1976 pp. 69–77.
 In Chinese philosophy, the concept of yin-yang, which is often called "yin and yang", is used to describe how seemingly opposite or contrary forces are interconnected and interdependent in the natural world; and, how they give rise to each other as they interrelate to one another. For more detailed information, see the Wikipedia article for "Yin and Yang