A Simple Guide to Chaos Theory (2024)
Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. This sensitivity is often referred to as the "butterfly effect," where small changes in the initial state of a system can lead to vastly different outcomes.
Key concepts in chaos theory include:
- Nonlinearity: Small changes can have large effects.
- Feedback loops: Outputs of a system can influence its inputs.
- Fractals: Complex patterns emerge from simple rules.
We recently asked Copilot to help us understand the butterfly effect better by using a simple high school algebra function, used in a feedback loop. See what he came up with: The Chaos Game!
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Additional, Deeper Perspective
Chaos: The Science of the Butterfly Effect (2020)
Sensitive dependency on initial conditions: The exact present exactly predicts the future, but the approximate present doesn't approximately predict the future.