No! It is deterministic. If you start with the *exact* same number, you get the exact same path. The chaos comes from the fact that we can't measure anything exactly.

What are the attractors?

They represent the valid states of the system (e.g., 'Stormy' vs 'Sunny'). The weather flips between these regimes unpredictably.

Is this the movie with Ashton Kutcher?

Yes, but the math is better than the plot.

The Butterfly Effect

Visualizing sensitive dependence.

📜 The Origins

Edward Lorenz discovered that changing a startup variable by 0.0001 changed his entire weather simulation. This is the 'Butterfly Effect'—a hurricane caused by a distant wing flap.

🚀 Master the Tool

Watch two simulations start almost perfectly synced. As time passes, see them violently diverge into completely different paths, proving that long-term prediction is impossible.

The Butterfly Effect Simulator

See how a microscopic difference (0.0001) in starting conditions leads to completely different outcomes.

System A: Start + 0.0000

System B: Start + 0.0001

Synchronization100% Match

Systems are effectively identical.

Sensitive Dependence

This is the Lorenz Attractor, a set of differential equations originally intended to model weather patterns.

Edward Lorenz found that rounding off a variable from .506127 to .506 completely changed the 2-month weather forecast. This proved that long-term prediction of chaotic systems (like weather or the stock market) is impossible.

The Butterfly Pattern

Notice how the trails never cross themselves, and they stay confined within a specific shape (the "Attractor").

Even though we can't predict exactly where the particle will be at time T, we know for sure it will be somewhere on the butterfly's wings. This is the difference between "Randomness" and "Chaos".

The Lorenz Attractor

This is the "Face of Chaos." In 1963, Edward Lorenz tried to model atmospheric convection using three simple differential equations. He discovered that the system never settled down. It orbited two invisible points (the "eyes" of the butterfly wings) forever, never crossing the same path twice.

Sensitive Dependence

This tool runs two simulations side-by-side. * Blue Dot: Starts at X = 1.000. * Red Dot: Starts at X = 1.001.

For the first few seconds, they look locked together. Then, slowly, they drift. Suddenly, they are on opposite sides of the screen. This proves that long-term weather prediction is impossible. We can never measure the current temperature of every atom on Earth with infinite precision, so the errors will always explode.