Please no butterfly analogies.
In: Mathematics
Chaos Theory is essentially studying equations where the assumption that changing the equation a small amount will lead to a small change in the result is broken. The goal is to determine where this starts to happen.
If you do some sort of experiment, you’d expect that if you repeat the experiment with the starting point altered slightly, then you’d get a slightly different result. Chaotic systems don’t follow that.
The first sort of step is finding things called bifurcations. Imagine there’s an equation that tells you the elevation of your next step, based on the elevation of your current step, while walking on uneven ground. A bifurcation would occur if there was a cliff for you to step off of. One step back, and the difference between the elevation of your feet would be small. Step off the cliff, huge change.
An actual example of a bifurcated system would be a rocket trying to escape from Earth’s gravity. Below escape velocity, the rocket comes back down to earth. Above it, it goes off into space.
A chaotic system has a certain point where you start getting those sudden huge changes *everywhere*. It might not be immediate, but changing one of those parameters, or where you start out, will lead to a result that you *cannot* predict just by knowing what happened when you started out close to it.
Source:BScH in Mathematical Physics, MSc in Applied Math.
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