There's a billion neato mathematical curiosities if we're talking about space ;-)
All could have literary analogies, easily.
Ever heard of the Kirkwood gaps? So there's this belt of asteroids between Mars and Jupiter, the Main Belt, but they're not evenly distributed. There are certain gaps, where no astroids exist, and "enhancements", where the astroids are clustered in concentration. The location of the gaps is due to 3-body physics, and therefore directly related to chaos theory.
If you take the region of the Main Belt where the mean motion of the asteroids is half the mean motion of Jupiter, a region known as the 2:1 Resonance Region, there are no astroids. If you somehow "placed" an astroid in this region, the eccentricity, e, would vastly increase until the asteroid was in the same orbit as Mars, and either collided or was thrown out.
Def'n of eccentricity
But, if you take the 3:2 Resonance Region, the eccentricity remains stable, and asteroids can survive here for long periods of time, and therefore they cluster.
Bottom line, part of chaos theory says that when you change the initial conditions no matter how little (like, the initial conditions for how the earth reacts with the sun might be hinged on what side of your fridge you keep the jam), the results vary wildly, exponentially. BUT, there are FAMILIES of solutions! It's not RANDOM, but it's chaotic.
And guess what this discovery gave us?
Fractals. Mandlebrot figured that the dimensions in a chaotic system had to be fractionated. So you can represent many complex chaotic systems with a fractal.
And how does this relate to a butterfly flapping its wings? So you'll always be informed at parties, a butterfly flaps its wings in New York, which changes Earth's "initial conditions" to such a small degree, but chaos theory takes over and "magnifies" this change in conditions exponentially, and it rains in Japan. Something big begat by something miniscule.