Physics 123: Introduction to Fractals and Chaos


For questions and comments, e-mail 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.

Students' Web Pages

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:
 SIERPINSKI SQR_GRAPHICAL_ITER  BOX COUNTING DIMENSION 
DIVIDER DIMENSION   MAY MAP PLOT  LOGISTIC LIST
LOGISTIC PLOT   GRAPHICAL ITERATION OF LOGISTIC MAP  BIFURCATION LOGISTIC
SIERPINSKI GASKET PICTURE   COLLAGE THEOREM FOR FERN  OAK LEAF RANDOM
OAK LEAF DETERMINISTIC   MANDELBROT1 M-SET WITH ORBITS 
M-SET WITH JULIA SETS  LORENTZ 2D  LORENTZ 3D 
 ROSSLER ATTRACTOR LORENTZ ERROR PLOT  M-SET 3D 
 M-SET WITH ZOOM M-SET BOUNDARY SCAN  RANDOM VS LOGISTIC TIME SERIES 
RANDOM VS. LOGISTIC PHASE MAP  3M ATTRACTOR RECONSTRUCTION 2-D  3M ATTRACTOR RECONSTRUCTION 3-D 
 FORCE DATA    


PHYSICS 123 SCHEDULE

SPRING 2002

PHYSICS 123, Introd. to Fractals and Chaos Professor Ben Szapiro
Tue-Thu 11:00-12:15 WL 225-Ext. 1858
WL 227 e-mail: bszapiro@sewanee.edu
MON TUESDAY WED THURSDAY FRI
CLASS 1 (1/15) CLASS 2 (1/17)
Introduction. Course's Overview and Toolkit.

Iteration & Feedback.

Camera/Monitor Video Feedback.

Video Feedback Project

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

Sierpinski gasket , Sierpinski Carpet ,Menger Sponge

Similarity and Box Counting Dimension.

Richardson Plots

Introd. to TRUEBASIC programming. Program ITERATE

Graphical Iteration SQRT

Program SIERPINSKI PICTURES

 

Measurement of coastal and river lengths. Log-log plots.

ASSIGNMENTS 1-1 to 1-6

CLASS 5 (1/29) CLASS 6
Fractal dimension D of leaves.

Koch Curve Program

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.

FRACTAL FRACTAL

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 non-linear systems.
Complexity and self-organization. Cellular automata. Discrete vs. continuous equations. The Logistic Equation.
CLASS 11 (2/19) CLASS 12

Program LOGISTIC. Regimes, bifurcation diagrams.

Graphical Iteration for Logistic Equation. Java Applet

BIFURCATIONS

QUADRATIC MAP

Logistic Equation using Excel Macro

Bifurcation Diagram using Excel Macro

Period doubling route to Chaos.

Feigenbaum's universal constant.

Divergence of nearby orbits. Folding and stretching.

Short and long term predictions.

Stretching and folding DEMO.

CLASS 13 (2/26) CLASS 14

MY FIRST WEB PAGE

Chaotic systems: Dripping Faucet Experiment.

Chaotic systems: The Driven Pendulum

ASSIGNMENTS 2-1 to 2-5

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

MID SEMESTER TEST

Chaotic systems: Magnetic Toy Experiment,
RLC-diode circuit . Lyapunov exponents.
Spring
CLASS 17 (3/12) Vacation NO CLASS

The Mandelbrot Set . M-set Applet

M-SET 3D, M-Set Features

Julia Sets. Julia Sets Applet

SPRING BREAK
Program MANDELBROT.
EXCEL VBA MACRO FOR M-SET
NO CLASS NO CLASS

SPRING BREAK

SPRING BREAK

W

Good
CLASS 18 (3/26) Last Drop Day CLASS 19 Friday

Weather prediction:

LORENTZ EQUATIONS

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 self-organization.
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

DLA Java Applet

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:

Mary Priestley: Lichens' Fractal Geometry

 

William Hooker: Fibonacci's Number

Presentation of Students' projects:

Cesar Mendez: Chua's Circuit

 

Phillip Suggs: Earthquake Modeling

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 (Mid-Sem., Final): 50%
NOTE: The course has a Web page in the Sewanne Physics Department. The address is: http://www.sewanee.edu/physics/Physics123.html

 

 

PROJECT TOPICS

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 Belousov-Zhabotinsky reaction (Roux, Physica D 7, 1983)
4 Taylor-Couette flow
5 Rayleigh-Benard convection
6 Chaos and non-linear 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 ABCDE-model)
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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SOME LINKS TO CHAOS

 

Interesting Web Sites:

 Dynamical Systems and Technology Project Fractal Domains Gallery  The Chaos Hypertextbook 
 The TRUE BASIC FREE Software  Fractals (Paul Bourke) Web BASIC Reader to RUN Programs 
MANDELBRAIN  MANDELMOVIE  FRACTAL DIMENSION CALCULATOR