Physics 123: Introduction to Fractals and Chaos
For questions and comments, email me at: bszapiro@sewanee.edu
For some DEFINITIONS click here.
For project TOPICS click here.
For SCHEDULE of classes click here.
For PREVIOUS semesters click here.
PageMill Graphics Instructions
To access your assigned folder
For chaos and fractals websites links click here.
To play the CHAOS GAME (Java Applet) click here: CHAOS GAME
Java Applet for Driven Pendulum
TRUEBASIC Version of Driven pendulum
SOME "BASIC" TRUE BASIC STATEMENTS
PROGRAMS TO COPY/PASTE AND RUN IN TRUE BASIC: 
SPRING 2002
PHYSICS 123, Introd. to Fractals and Chaos  Professor Ben Szapiro  
TueThu 11:0012:15  WL 225Ext. 1858  
WL 227  email: bszapiro@sewanee.edu  
MON  TUESDAY  WED  THURSDAY  FRI 
CLASS 1 (1/15)  CLASS 2 (1/17)  
Introduction. Course's Overview and Toolkit.  Iteration & Feedback. 

The Chaos Game. Randomness and Determinism. Play Games: Chaos, Towers of Hanoi 

CLASS 3 (1/22)  CLASS 4 (1/24)  
Introduction to Fractal Geometry. Famous Fractals: Cantor Set,Koch curve, Koch Snowflake 

Introd. to TRUEBASIC programming. Program ITERATE Graphical Iteration SQRT


CLASS 5 (1/29)  CLASS 6  
Fractal dimension D of leaves. 
Fractal organization in biology. Methabolic rate scaling laws. 

Measurement of D for paper wads.  Branching patterns in artherial, lung and kidney systems.  
CLASS 7 (2/5)  CLASS 8  
DNA encoding and fractals. Lindenmayer systems.  Iterated Function Systems (IFS). Program IFS. 

Collage Theorem: Barsnley's Ferns  Computer generated fractal images and movies.  
Last  
Drop  CLASS 9 (2/12)  CLASS 10  
Day  The Game of Life. Rules for survival, persistent patterns.  Introduction to Chaos: linear vs nonlinear systems.  
Complexity and selforganization. Cellular automata.  Discrete vs. continuous equations. The Logistic Equation.  
CLASS 11 (2/19)  CLASS 12  
Program LOGISTIC. Regimes, bifurcation diagrams. 
Logistic Equation using Excel Macro Bifurcation Diagram using Excel Macro 

Divergence of nearby orbits. Folding and stretching.  Short and long term predictions. Stretching and folding DEMO. 

CLASS 13 (2/26)  CLASS 14  
Chaotic systems: Dripping Faucet Experiment. 
Chaotic systems: The Driven Pendulum 

Concept of Strange Attractors.  Definition and Characterization of (Deterministic) Chaos.  
Mid  
Semester  CLASS 15 (3/5)  CLASS 16  
Last day to Drop/Add without Approval  Chaotic systems: Magnetic Toy Experiment,  
RLCdiode circuit . Lyapunov exponents.  
Spring  
CLASS 17 (3/12)  Vacation  NO CLASS  
The Mandelbrot Set . Mset Applet Julia Sets. Julia Sets Applet 
SPRING BREAK  
Program MANDELBROT.  
EXCEL VBA MACRO FOR MSET  
NO CLASS  NO CLASS  
SPRING BREAK 
SPRING BREAK 

W 
Good  
CLASS 18 (3/26)  Last Drop Day  CLASS 19  Friday  
Weather prediction: the Lorentz attractor, the "Butterfly" Effect. Measuring Chaos 
Philosophical implications of Chaos. Determinism vs. free will. PROJECT'S DRAFT DUE 

Example: Modeling of outbreak of war.  
CLASS 20 (4/2)  CLASS 21  
Chaos in human interactions: modeling of relationships.  Levy's distribution of prices. Example:LOVE/HATE modeling Example: Flour beetles modeling 

Scaling laws in nature. Zipf's law in linguistics.  Hurst exponent. Sandpiles and selforganization.  
Prereg  
Begins  CLASS 22 (4/9)  CLASS 23  
Chaos and Art. Surprise and regularity.  3 Experiments: Dripping Faucet Chaotic Circuit Driven Pendulum 

POSTER DUE  
CLASS 24 (4/16)  CLASS 25 (4/18)  
Definitions of chaotic behavior, strange attractors, Lyapunov Exponent, Requirements for chaotic behavior. Time Series Analysis, Delay Maps Assignment 2 is due PROJECTS: WEB PAGE POSTING DUE 
Preparation of Students' projects  
CLASS 26 (4/23)  CLASS 27 (4/25)  
Presentation of Students' projects: 
Presentation of Students' projects: 

CLASS 28 (4/30)  Reading day (5/2)  
Presentation of Students' projects:
Clay O'Gwin/John Robbins: Modeling of the Stock Market

Final Exam: Saturday, May 4, 9 AM 

LAST CLASS! EVALUATION AND REVIEW.  ENJOY YOUR SUMMER!  
Bibliography:  GRADING:  
1) Fractals and Chaos, Addison, IOP 1997  Student's Project: 25%  
2) Chaos under control, Peak & Frame, Freeman, 1994  Classwork: 25%  
3) Chaos: Making a New Science, Gleick, Viking, 1987 ...Buying Info 
Two tests (MidSem., Final): 50%  
NOTE: The course has a Web page in the Sewanne Physics Department. The address is: http://www.sewanee.edu/physics/Physics123.html  
LIST OF POSSIBLE TOPICS FOR CHAOS CLASS PROJECT  
Students are expected to present a two page draft describing their intended project  
by March 27, a Web page poster display by April 10, and a 15 minutes presentation  
to the class to be scheduled starting April 17. You will be graded on the quality of the work and of the  
presentation. An extra 1/4 final letter grade will be awarded to the top three projects.  
This long list is not exhaustive, and you are welcome to discuss with me other possible  
topics of your interest.  
TOPIC:  Student Name  
1  Buckled beam experiment (Brunsden et al., 1989)  
2  Chua's circuit (Madan, 1993)  
3  BelousovZhabotinsky reaction (Roux, Physica D 7, 1983)  
4  TaylorCouette flow  
5  RayleighBenard convection  
6  Chaos and nonlinear models in economics (Creedy/Martin, 1994; Goodwin, 1990)  
7  Cellular automaton modeling of collective behavior  
8  Time series analysis of price fluctuations  
9  Lindenmayer systems for modeling plant growth (Prusinkiewicz & Lindenmayer, 1990)  
10  Chaos Language Algorithm (Goertzel,1995)  
11  Mathematical modelling of the AIDS epidemic (Stanley, 1989)  
12  Modelling of rumor propagation  
13  Implications of Chaos theory for theological issues (Russel/Murphy/Peacocke, Vatican,1995)  
14  Dynamics of friendships (Levinger's ABCDEmodel)  
15  Diffusion limited agregation processes (spread rates of fires on forests, etc)  
16  The Mandelbrot Set  
17  Chaos implications for futures forecasting (Hansson, Futures 23:1,1991)  
18  The mathematical theory of war and peace (Richardson's arms race model, Saperstein)  
19  Budgets as dynamical systems (Kiel/Elliot, Journal of Public Admin. Reserarch,1992)  
20  The fractal structure of the universe (Coleman/Pietronero, Phys. Rep. 213, 1992; Gurzadyan)  
21  Fractal analysis in cardiology (Denton et al., Am. Hearth J., 120, 1990)  
22  Fractal image compression techniques using Iterated Function Systems (M. Barnsley)  
23  A geometric model of ideologies (Zeeman,E.C., 1976,1979)  
24  Controlling chaos and its use on message encoding/decoding.  
25  Fractal description of urban growth (Batty, M. , Nature 377,1995)  
26  Fractal geometry in architecture and design (Bovill, C., 1996)  
27  Fractals: a new aesthetic (Briggs,J. , 1992)  
28  Microbial dynamics on soil based on fractal geometry (Crawford et al., Geoderma 56, 1993)  
29  Fractals in chemistry (Harrison, A., 1995)  
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Interesting Web Sites: