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Unit 13

The Concepts of Chaos

Planet Planet

The flapping of a butterfly's wings over Bermuda causes a rainstorm in Texas. Two sticks start side by side on the surface of a brook, only to follow divergent paths downstream. Both are examples of the phenomenon of chaos, characterized by a widely sensitive dependence of the future on slight changes in a system's initial conditions. This unit explores the mathematics of chaos, which involves the discovery of structure in what initially appears to be randomness, and imposes limits on predictability.

Unit Goals

Video Transcript

Video

Most of us learned at an early age how an apple falling from a tree... inspired Isaac Newton to describe how the universe behaves by certain predictable rules. But what about when the universe doesn't behave so... predictably? Can mathematics explain the often unpredictable behavior of the physical world?

Textbook

Textbook

The real world is one in which small differences in the initial circumstances of a sequence of events can indeed have a significant effect on the final outcome. The mathematical tools that we need to understand this sort of real-world phenomenology come from the realm of chaos theory.


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