1. HONR 300/CMSC 491 Chaos (Flake, Ch. 8) Prof. Marie desJardins, March 2, 2011 1Chaos 3/2/11

2. Key Ideas Visualizing chaos Time series graph State space graph Types of regimes: Fixed points Limit cycles Quasiperiodic Chaos Properties of chaos Determinism Sensitivity Ergodicity Chaos 3/2/11 2

3. As Randall Munroe Sees It Chaos 3/2/11 3 xkcd.com

4. Fixed Point Behavior Chaos 3/2/11 4

5. Limit Cycle Chaos 3/2/11 5

6. Complex Limit Cycle Chaos 3/2/11 6

7. Chaos 7

8. Bifurcations of the Logistic Map Chaos 3/2/11 8

9. Properties of Chaos Determinism Sensitivity to initial conditions Ergodicity Chaos 3/2/11 9

10. If you don’t believe in “the butterfly effect” or the conclusion of The Sound of Thunder, consider these thoughts: The Game of Life is much simpler than the world. Yet changing the state of just one cell in the initial configuration can lead to a completely different state of the world in a very small number of iterations. Millions of years is a really long time for the “compound interest” to take effect. And remember the old saying: For want of a nail the shoe was lost. For want of a shoe the horse was lost. For want of a horse the rider was lost. For want of a rider the battle was lost. For want of a battle the kingdom was lost. And all for the want of a horseshoe nail. Chaos 3/2/11 10

11. Hang onto your hats... Next week we’re going to see the fractal dimension rear its Hydra- like head again! Chaos 3/2/11 11