A bound pair of point masses can trace a perfect ellipse forever. Newton
solved that two-body problem in 1687. Add a third and there is no
general closed-form solution. Poincaré revealed the problem’s chaotic,
non-integrable structure.
What should I watch for?
That does not mean the motion is random. It obeys one short law exactly.
It means long-range prediction becomes practically limited: two starts
that differ by a hair can end up in completely different places.
You are watching a bound, non-hierarchical random throw —
three equal masses close enough that none begins as the distant outsider.
This class of triple usually decays into a tight binary plus one escaping
body. The chaos is in which body leaves, when, and what pair survives.
Why opposite directions? A close encounter gives the escaper
positive energy while the surviving binary becomes more tightly bound.
The whole system starts with zero net momentum, so the binary’s center
of mass must recoil opposite the escaping body. Chaos creates the encounter;
conservation laws shape the ending.
Clear returns the selected arrangement and controls to their defaults,
stopped at time zero so you can configure a fresh experiment. Knock a
twin creates a comparison universe and gives one body a large sideways
kick so you can see the same law react to a deliberately different start.
Then the real surprise. A few exact, repeating solutions do exist
— they are just infinitely
rare. Disturb the figure eight and little happens. Disturb
Euler’s line, which is equally exact, and it dies. Same law,
opposite outcomes.