We will not fully describe chaos, but
it is the property
that causes a system to have
super-sensitivity to initial conditionsAND to evolve in a very complex way.
A chaotic system, even though
completely obeying
determinism in principle, evolves eventually
in completely unpredictable way as a usual rule.
The usual rule is because you can never exactly calculate continuous quantities, and so at some
point calculation error will cause you to leave the path of true evolution.
At that point, the super-sensivitivty and complex evolution conditions lead the
true evolution far away from the calculated evolution.
In the cartoon, two systems
start from nearly the same
initial conditions.
But since the systems are
chaotic, their evolution eventually
becomes completely different.
Unless, the initial conditions
were exactly the same, very different evolution must occur eventually.
Many systems actually exhibit chaos.
But we don't see chaos
much in the human world.
We don't build our machines to be chaotic.
No one wants a chaotic car engine.