For schedule of fall '99 classes click HERE.

For questions and comments, e-mail me at: bszapiro@sewanee.edu

For some DEFINITIONS click here.

For project topics click here.

For previous semester (spring '98) schedule click here.

• Go to Chooser,
• Select 00AngelNet Zone,
• Click on AppleShare icon
• Select "06 -Sewanee WWW" server,
• Login using your student's ID; the password is also the student's ID
• Double click the "WWW Data" Icon and open the "Web Server" Folder.
• Open the folder "Phy_Students", your folder should be unlocked.
• Open Adobe PageMill to create/edit your web page.
• You are encouraged to change the password to one of your choice.

For chaos and fractals websites links click here.

To play the CHAOS GAME (Java Applet) click here: CHAOS GAME

To experiment with a chaotic driven pendulum (Java Applet) click here :Complicated Behavior

PROGRAMS TO COPY/PASTE AND RUN IN TRUE BASIC:

SOME "BASIC" TRUE BASIC STATEMENTS:

PROGRAM SIERPINSKI

PROGRAM KOCH CURVE

PROGRAM SQR_GRAPHICAL_ITER

PROGRAM BOX COUNTING DIMENSION

PROGRAM DIVIDER DIMENSION

PROGRAM MAY MAP PLOT

PROGRAM LOGISTIC LIST

PROGRAM LOGISTIC PLOT

PROGRAM GRAPHICAL ITERATION OF LOGISTIC MAP

PROGRAM BIFURCATION LOGISTIC

PROGRAM SIERPINSKI GASKET PICTURE

PROGRAM COLLAGE THEOREM FOR FERN

PROGRAM OAK LEAF RANDOM

PROGRAM OAK LEAF DETERMINISTIC

PROGRAM MANDELBROT1

PROGRAM M-SET WITH ORBITS

PROGRAM M-SET WITH JULIA SETS

TEST No.1 : MID SEMESTER TEST

PROGRAM LORENTZ 2D

PROGRAM LORENTZ 3D

PROGRAM ROSSLER ATTRACTOR

PROGRAM LORENTZ ERROR PLOT

PROGRAM M-SET 3D

PROGRAM M-SET WITH ZOOM

PROGRAM RANDOM VS LOGISTIC TIME SERIES

PROGRAM RANDOM VS. LOGISTIC PHASE MAP

PROGRAM 3M ATTRACTOR RECONSTRUCTION 2-D

PROGRAM 3M ATTRACTOR RECONSTRUCTION 3-D

PROGRAM FORCE DATA

PHYSICS 123 SCHEDULE

	PHYSICS 123, Introd. to Fractals and Chaos		Professor Ben Szapiro
	Tue-Thu 9:30-10:45		WL 225-Ext. 1858
	WL 227		e-mail: bszapiro@sewanee.edu
MON	TUESDAY	WED	THURSDAY	FRI
			CLASS 1 (8/26)
			Introduction. Course's Overview and Toolkit. The Chaos Game. Randomness and Determinism.
			Three points, 1/2 Chaos Game.
	CLASS 2 (8/31)		CLASS 3 (9/2)
	Iteration & Feedback. Camera/Monitor Video Feedback. Introd. to Fractals. Koch curve, Sierpinski gasket & carpet		Similarity and Box Counting Dimension. Richardson Plots
	Introd. to TRUEBASIC programming. Program ITERATE		Measurement of coastal and river lengths. Log-log plots.
	CLASS 4 (9/7)		CLASS 5 (9/9)
	Fractal dimension of Sewanee Campus, leaves, dendrites.		Fractal organization in biology. Methabolic rate scaling laws.
	Measurement of D for paper wads.		Branching patterns in artherial, lung and kidney systems.
	CLASS 6 (9/14)		CLASS 7 (9/16)
	DNA encoding and fractals. Lindenmayer systems.		Iterated Function Systems (IFS). Program IFS.
	Barsnley's Ferns and the Collage Theorem		Computer generated fractal images and movies.
Last
Drop	CLASS 8 (9/21)		CLASS 9 (9/23)
Day	The Game of Life. Rules for survival, persistent patterns.		Introduction to Chaos: linear vs non-linear systems.
	Complexity and self-organization. Cellular automatons.		Discrete vs. continuous equations. The Logistic Equation.
	CLASS 10 (9/28)		CLASS 11 (9/30)
	Program LOGISTIC. Regimes, bifurcation diagrams.		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 12 (10/5)		CLASS 13 (10/7)
	Chaotic systems: Dripping Faucet Experiment.		Chaotic systems: Bouncing Ball and Buckling Beam Experiments.
	Concept of Strange Attractors.		Definition and Characterization of (Deterministic) Chaos.
Mid
Semester	CLASS 14 (10/12)		CLASS 15 (10/14)
Drop/Add	MID SEMESTER TEST		Chaotic systems: Magnetic Toy Experiment,
			RLC-diode circuit . Lyapunov exponents.
FALL BREAK	NO CLASS		CLASS 16 (10/21)
			The Mandelbrot Set. Julia Sets.
			Program MANDELBROT.
	CLASS 17 (10/26)	Drop	CLASS 18 (10/28)	Friday
	Weather prediction: the Lorentz attractor, the "Butterfly" Effect. PROJECT'S DRAFT DUE		Philosophical implications of Chaos. Determinism vs. free will.
	Example: Modeling of outbreak of war.
	CLASS 19 (11/2)		CLASS 20 (11/4)
	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.
	CLASS 21 (11/9)		CLASS 22 (11/11)
	Chaos and Art. Surprise and regularity.		Brownian motion. Chaos and noise. Power spectral analysis.
	Chaos and medicine. L-systems for plant growth. POSTER DUE		DLA. Time series analysis. The "colors" of noise.
	CLASS 23 (11/16)		CLASS 24 (11/18)
	SPECIAL TOPICS		SPECIAL TOPICS
	CLASS 25 (11/23)		NO CLASS
	Presentation of Students' projects:		Thanksgiving Break
	CLASS 26 (11/30)		CLASS 27 (12/2)
	Presentation of Students' projects: DONEV'S PROJECT		Presentation of Students' projects: KRAUSE'S PROJECT SHAFFER'S PROJECT
	CLASS 28 (12/7)		FINAL EXAM (12/9) 2:00 PM
	LAST DAY OF CLASSES. EVALUATION AND REVIEW		ENJOY YOUR BREAK!
	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		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 30, a Web page poster display by April 13, and a 15 minutes presentation
	to the class by April 20. 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)
30
31
32
33
34
35
36
37
38

LINKS TO CHAOS

LORENTZ