Chaos

In mathematics chaos is the idea that some things that appear totally random may actually have underlying patterns.

For example: increasing the flow from a hose may start as a regular drip, then become a chaotic flow of drips, then may go back to a more regular flow.

Weather is another example. Computer models can sometimes predict the weather well. But other times it can be "unstable" and something as small as a butterfly flapping its wings could lead to big changes in a few days. This is called the "butterfly effect".

How? Maybe the flap of its wings causes a tiny change in air flow that shifts a few raindrops a short while later, and this causes the wind to shift very slightly so that three hours later a cloud goes the other side of a mountain range, and so on.

This is why, despite advanced science and powerful computers, the weather can still be hard to predict.

Usually though small changes don't have this effect, but in some cases they can.

Certain systems behave like that, including weather, turbulence (such as some streams of water), the stock market, and more.

Here we see chaos in something as simple as two pendulums connected together: