Geology - Physics 30

 

Fractals, Chaos and Complexity

 

Winter Quarter, 2009

 

John Rundle

Professor of Physics, Geology and Engineering

 

At Left:  A Map of the Internet

 

(http://www.caida.org)

 

Course Syllabus

 

Get Adobe Acrobat Reader

 

Please note that homework can be turned into Professor Rundle either in class, or at his office in 534B Physics-Geology by 5:00 pm on the due date.

 

Note:  The material in the book by Schoeder is more advanced, and is provided
for students who want to further explore the topics

 

Week

Topic

Reading Assignment

Chapter/Section



Homework/Lab Assignment

 

Homework Due Date

1  January 5

 Introduction - Exploring Fractals and Chaos

Peak & Frame

Chapter 1, pg 5-17

 

Schroeder

Chapter 1, 1-25

Explore Frame Web Site

Frame Web Site:

1 - 1D

 Monday Jan 12
2  January 12

Fractals - Fractal Generators & Iterated Function Sets

Intro to Probability

Peak & Frame

Chapter 1, pg 18-40

 

Schroeder

Chapter 1, 25-49

Scaling Laws

Homework 1

Chaos_Game

Friday January 16
3  January 19 Fractals - Cont.

Fractal Dimensions

Peak & Frame

Chapter 2, All

Begin Chapter 3

Schroeder

Chapter 9

 

Fractal_Summary

 Homework 2 Wednesday January 28
4  January 26

Fractals, Power Laws, Introduction to Chaos

 

Peak & Frame

Chapter 3, All

Begin Chapter 4

 

Schroeder

Chapter 3

Chapter 10, 211-225

Bruce Malamuds Talk

    
5  February 2 Chaos

Iterated Maps
Logistic & Tent Maps
Attractors & Fixed Points

Peak and Frame

Chapter 4, 5

 

Schroeder Chapter 12

pp 268-286

pp 89-294


NY Times Article:

"In Natures Casino"  

 Homework 3 Friday February 6
6  February 9

Complex Fractals Mandelbrot Set

Peak and Frame

Chapter 7
Chapter 8

 

Schroeder

Chapter 11, 237-245
Chapter 12, 295-299

Homework 4

1-paragraph description of project - see syllabus for some examples of possible projects

Friday February 13
7  February 16


Mandelbrot (cont.)

Fractal Boundaries

Newton's Method
  

Schroeder
Chapter 17, 371-386


Computation in CAs

 
8  February 23  

Cellular Automata
Artificial Life
Theory of Computation

 

 

Peak and Frame
Chapter 9

Schroeder
Chapter 10, 232-236

 

  HW 5 & Problem 3 Ans.

   Monday March 2
9  March 2

 

Neural Networks

Cluster Growth
Probability

Probability 1

Probability 2

 Homework 6 Monday March 16
10  March 9


Percolation
Pattern Formation Examples and Applications

Course web site
Ian_Dobsons_Talk

  Course Projects are Due on March 20
11  March 16  Summary & Discussion  
12 March 17        

Final Exam March 20, 10:30 am -12:30 pmRoom 185 PHYGEO

(We will not have a final - last day to turn in homeworks and projects)



Please hand all outstanding work in by March 20  5:00 pm