1 gem2505 frederick h. willeboordse frederik@chaos.nus.edu.sg taming chaos

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GEM2505

Frederick H. Willeboordsefrederik@chaos.nus.edu.sg

Taming Chaos

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Briefing and Introduction

Lecture 0

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This picture was taken in 2371 on board of the starship Enterprise and is, due to time distortions, a bit blurry. Who would have thought I’d end up in Singapore!

Frederick H. Willeboordse

S12 #03-06

Dept. Physics

Specialized in Complex Systems and Chaos

E-mail: phyfhw@nus.edu.sg

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Why the module?

In order to gain an understanding of nature in a way that’s rather different from the traditional approach.

Understanding

We’ll need some Mathematics but it will be limited and should generally not exceed secondary school level.

How about Math?

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A: 2 – 4 lecture hours per weekB: 1 tutorial hour per weekC: 0 lab work per weekD: 1 - 3 hours for assignments per weekE: 4 hours of preparation work per week

The total workload for this GEM is 10 hours per week.

Of course, for this module, items D&E can overlap.

Workload

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Lectures: 2 – 4 hours per week for a total of 26 lecture hours

(these include the in-class quizzes)

Mondays & Thursdays 16:00 – 18:00 as announced

Tutorials:4 times 1 hour as announced

Discussion Sessions:3 times: As announced

Schedule

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Schedule Jan 12, 2004 Lecture 0

Jan 15, 2004 Lecture 1

Jan 19, 2004 Lecture 2

Jan 26, 2004 Lecture 3 SCT1

Jan 29, 2004 Lecture 4

Feb 5, 2004 ICT1

Feb 9, 2004 Lecture 5

Feb 12, 2004 Lecture 6

Week of Feb 16, 2004

Reading Assignments

SCT2

Feb 23, 2004 Lecture 7

Feb 26, 2004 Lecture 8

Mar 1, 2004 ICT2

Mar 4, 2004 Lecture 9

Week of Mar 8, 2004

Reading Assignments

SCT3

Mar 15, 2004 Lecture 10

Mar 22, 2004 Lecture 11 SCT4

Mar 29, 2004 Lecture 12

Apr 1, 2004 ICT3

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All together there will be 10 quizzes with which you can earn 5 points each for a total of 50 points.The final exam will be open book and count for 50 points as well.

Quizzes: 10 * 5 pointsExam: 1 * 50 points

Assessment

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During most of the lectures, there will be a quiz. Usually, I’ll try to do the quiz around the middle of the lecture so that you won’t miss it if you come late.

Discussion of Previous Quiz

Discussion of Assignment

First Part of the Lecture

Quiz

Applets and Animations

Second Part of the LectureLecture

Lectures

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Talk!

Tutorials

There are two types of tutorials:

In-class

Small group

Register after the lecture.

last semester’s class

The goal of the tutorial is to have a free and open discussion.

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All the lecture notes as well as other relevant material can be found on my web site at:

http://chaos.nus.edu.sg/Teaching/GEM2505/

There are no required text books!

Recommended Book:James Gleick - Chaos

Text Books

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There will be three chapters around the broader theme of chaos – some changes may still be made!

I. The Essence of Chaos II. Fractals, CAs & NetworksIII. Understanding Chaos

Does organization need regularity?

Course Contents

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The Butterfly Effect The Clockwork Syndrome

Course Contents

I. The Essence of Chaos

=?

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The Cantor Set The Mandelbrot Set

Course ContentsII. Fractals

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Course Contents

The Game of Life A New Kind of Science

II. Cellular Automata

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Course Contents

The Internet The Cell

II. Scalefree Networks

What do they have in common?

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The Logistic Map Strange Attractors Universality & Randomness

Course Contents

III. Understanding Chaos

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Some Examples of ChaosThe motion of the planets is chaotic. In fact, even the sun, earth moon system cannot be solved analytically!

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Can such a spot survive in a chaotic environment?Or perhaps, can it exist without chaos?

Some Examples of ChaosThe red spot on Jupiter:

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One of the great successes of experimental chaos studies.

A spot is reproduced.

Note: these are false colors.

Some Examples of ChaosAn experiment by Swinney:

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Waves representing the concentration of a certain chemical(s).These can assume many patterns and can also be chaotic

Some Examples of ChaosBeluzov-Zhabotinski reaction

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Some Examples of ChaosSatellite image of a river delta:

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Broccoli Romanesco is a cross between Broccoli and Cauliflower.

Some Examples of ChaosYummi!

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The venous and arterial system of a kidney

Some Examples of ChaosWould there be life without chaos?

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Our world is embedded in a dichotomy of order and chaos.It is possible to gain a qualitative understanding of chaos without too much mathematics.

Chaos is fun!

Summary