The Simple English Wikipedia answers your question better than anyone else has so far: [https://simple.wikipedia.org/wiki/Chaos_theory](https://simple.wikipedia.org/wiki/Chaos_theory)

Chaos theory is basically the underlying mathematics of how small changes to the beginning of a process can have drastically different outcomes, so that they seem random and unpredictable, yet there is an underlying determinism to the randomness.

A famously ridiculous example is the “butterfly effect” in which a butterfly flapping its wings in Europe can affect the weather weeks later in California. As Terry Pratchett wrote in the first footnote in *Witches Abroad*, scientists ought to be “finding that bloody butterfly whose flapping wings cause all these storms we’ve been having lately and getting it to stop.”

A real-world example that always fascinated me is one you can demonstrate yourself. You can do it with water dripping from a faucet but it works better with water dripping from a small spigot. At a low flow, the water has a steady drip, drip, drip, drip. Increase the flow rate slowly, and then you’ll notice a “bifurcation” where the drips double: drip-drip, drip-drip, drip-drip. Increase the flow rate more, and each double drip bifurcates into four drips, but typically faucets can’t resolve the time interval between drips. The point is, increase it a little bit more and you start getting drips falling out at seemingly random intervals. Here we have chaos, which happens in a range of flow rates. The sequence of random drips at one flow rate is completely different from the sequence at any other flow rates, even one that is nearly the same but not quite.

It seems random, but here’s the kicker. If you can measure all the time intervals between these random drips and plot a graph of one interval versus the last interval, you get a smooth curve. This means that the random drips are being determined by a fairly simply underlying rule. You have just applied chaos theory by finding determinism in randomness. If you care to see the scientific analysis, have a look at this paper: [https://nldlab.gatech.edu/w/images/f/f6/Royer_Caleb_PHYS6268_Royer_FinalPaper.pdf](https://nldlab.gatech.edu/w/images/f/f6/Royer_Caleb_PHYS6268_Royer_FinalPaper.pdf) – particularly the graphs near the end.

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