Slingshot
Every body here pulls on every other one by Newton's law and nothing else. Two galaxies pass and throw nearly half their stars into long tidal tails; three stars chase each other round a figure-8 for ever; a probe leaves a planet about 40% faster than it arrived. Through all of it the total energy stays put to within a few millionths of itself, measured live.
In 1687 Isaac Newton wrote down one rule: every mass pulls on every other mass, with a force that falls off as the square of the distance between them. For two bodies the rule solves completely — every orbit is an ellipse, a parabola or a hyperbola, and you can write down where a planet will be in a thousand years. Add a third body and that certainty is gone. In 1890 Henri Poincaré showed that the three-body problem has no general formula, and in doing so found the first glimpse of what is now called chaos.
What surprises is how much keeps still while everything moves. Planets swing in and out, galaxies shred, a flung rock dives past a star at ten times its starting speed, and yet two numbers never change: the total energy and the total angular momentum. The tiles under the sky track both, and the chart beside them shows the trade happening underneath — kinetic energy surging as bodies fall together, potential energy deepening by exactly the same amount, the gold line of their sum lying flat. When two bodies collide and merge, the energy count restarts, because real collisions turn motion into heat.
Some of the scenes are famous. In 2000 Alain Chenciner and Richard Montgomery proved that three equal stars can chase each other round a single figure-8 for ever, and the page times its period live against their value of 6.3259. The Lagrange scene shows the Trojan asteroids that share Jupiter's orbit, parked 60 degrees ahead and behind, seen from a camera that turns with the planet. The galaxy scene is the one Alar and Juri Toomre ran in 1972 to show that the long streamers of interacting galaxies are tides, not explosions.
And one is a trick engineers use every few years. A probe that passes behind a moving planet comes out faster relative to the Sun — Voyager 2 reached Neptune this way — while relative to the planet itself its speed in and out is the same. The page reads both numbers as the probe crosses the dashed ring. The speed was borrowed from the planet's orbit, which slows by an amount far too small to see.
One ant, one rule, no randomness — ten thousand steps of pure chaos, and then, out of nowhere, it starts building a road and never stops.