Spencer Hart Advisor: Gus Hart

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Presentation transcript:

Spencer Hart Advisor: Gus Hart Understanding Chaos Spencer Hart Advisor: Gus Hart

What is Chaos? noun 1. complete disorder and confusion. PHYSICS behavior so unpredictable as to appear random, owing to great sensitivity to small changes in [initial] conditions

What types of systems exhibit chaos? Non-linear systems Dripping faucet Weather Heart fibrillation

Simple Pendulum

Simple Pendulum

Physical Pendulum

Phase Space Plots

Effect of Driving Force

Effect of Driving Force

Low Driving Force

Low Driving Force

High Driving Force

High Driving Force

Is there any hope?

Attractors Attractor: “Physics: A set of physical properties toward which a system tends to evolve, regardless of the starting conditions of the system.” -thefreedictionary.com

The Chaos Game 6

The Chaos Game

The Chaos Game

The Chaos Game

The Chaos Game

The Chaos Game

Any Ideas?

Sierpinski Triangle

500000 Iterations

Fractal Nature Strange Attractor Approx. 81x zoom

Strange Attractor for Pendulum

Strange Attractor for Pendulum

Real life?