Sci 122 Telecourse Program 30 Entropy & Chaos

# Entropy & Chaos Program 30 Lesson 4.8

## 1. Introduction

 "Chaos rules the universe. Scientists call it 'ENTROPY'" "Everything is breaking down tending towards GREATER AND GREATER DISORDER." "It's great to be on the winning side."

## 13. Chaos

### 13.3. complex systems

#### 13.3.1. nonlinear systems have feedback 13.3.2. "The Butterfly Effect": An extremely small cause can have very large effects. A butterfly flapping its wings in Asia affect the weather worldwide.

##### 13.3.2.1. Lorenz's weather machine 13.3.2.2. rounded divergence 13.3.2.3. folklore 1

For want of a nail, the shoe was loss
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.

### 13.4. chaos

#### 13.4.3. attractors 13.4.4. values of functions can bifurcate and attain different states from tiny differences in values

##### 13.4.4.1. The Lorenzian Waterwheel

###### 13.4.4.1.1. simple device proves capable of surprisingly complicated behavior 13.4.4.1.2. long term behavior depends on how hard the driving force is, ie. on the intensity of the energy gradient 13.4.4.1.3. show on graph that Force is the slope of an energy vs. displacement graph 13.4.4.1.4. water pours into top bucket at steady rate 13.4.4.1.5. too slow --> top bucket doesn't fill enough to overcome friction so the wheel never turns 13.4.4.1.6. initial direction is extremely sensitive to initial position of top bucket

13.4.4.1.6.1. try balancing a credit card (not the budget) by standing it on end

#### 13.4.5. The Mandelbrot Set and Fractals

##### In the figures below, each picture represents an enlargement of the white frame in the pircute before it.

###### 13.4.5.3.8. Mandelbrot 8

This last picture is "pixelated" to save time. In reality the set can be "magnified" indefinitely with no loss of clarity.

##### 13.4.5.4. fractal folklore

Turtle upon turtle upon turtle.