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.
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 | |||
| 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. |
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The Chaos Game. Randomness and Determinism. Play Games: Chaos, Towers of Hanoi |
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| CLASS 3 (1/22) | CLASS 4 (1/24) | |||
Introduction to Fractal Geometry. Famous Fractals: Cantor Set,Koch curve, Koch Snowflake |
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Introd. to TRUEBASIC programming. Program ITERATE Graphical Iteration SQRT
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| CLASS 5 (1/29) | CLASS 6 | |||
| Fractal dimension D of leaves. |
Fractal organization in biology. Methabolic rate scaling laws. |
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| 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. |
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| 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. |
Logistic Equation using Excel Macro Bifurcation Diagram using Excel Macro |
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| Divergence of nearby orbits. Folding and stretching. | Short and long term predictions. Stretching and folding DEMO. |
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| CLASS 13 (2/26) | CLASS 14 | |||
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Chaotic systems: Dripping Faucet Experiment. |
Chaotic systems: The Driven Pendulum |
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| 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, | |||
| RLC-diode circuit . Lyapunov exponents. | ||||
| Spring | ||||
| CLASS 17 (3/12) | Vacation | NO CLASS | ||
The Mandelbrot Set . M-set Applet Julia Sets. Julia Sets Applet |
SPRING BREAK | |||
| Program MANDELBROT. | ||||
| EXCEL VBA MACRO FOR M-SET | ||||
| NO CLASS | NO CLASS | |||
SPRING BREAK |
SPRING BREAK |
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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 |
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| 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 |
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| 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 |
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| 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: |
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| CLASS 28 (4/30) | Reading day (5/2) | |||
Presentation of Students' projects:
Clay O'Gwin/John Robbins: Modeling of the Stock Market
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Final Exam: Saturday, May 4, 9 AM |
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| 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 | ||||
| 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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Interesting Web Sites: