Do a search for "Lorentz attractor". It's the result of an early numerical weather model.
The weather is a particular point on the twisted surface; it is impossible to calculate what point you'll reach at a given time, for reasons that you'll find in a search for "Lyapurnov exponent".
The climate is the butterfly shape. If you run the simulation with different parameters, you can look and see how this changes.
The Lorentz equations are much simpler than a realistic weather model, but the same principles apply to the complicated models, and to the laws of physics that the atmosphere actually follows.
The weather is a particular point on the twisted surface; it is impossible to calculate what point you'll reach at a given time, for reasons that you'll find in a search for "Lyapurnov exponent".
The climate is the butterfly shape. If you run the simulation with different parameters, you can look and see how this changes.
The Lorentz equations are much simpler than a realistic weather model, but the same principles apply to the complicated models, and to the laws of physics that the atmosphere actually follows.