1

First Year Seminar:

Determinism, Chance and Chaos: a Visual Approach to Newtonian Mechanics

Fall 2016

October 11 to December 6, 2016 (starts in 6 weeks, open for enrollment)

9:00 AM-10:40 AM VAN-201

Instructor: Prof. Yannick Meurice

Our understanding of the laws of physics has generated many practical applications which

are part of everyday’s life. Surprisingly, it can also be used to generate objects that can be

considered as artistic. Emphasizing this aspect is a unique feature of this first year seminar.

The students will familiarize themselves with the visualization of the time evolution of

simple systems studied by physicists. They will start with very simple examples and work

their way progressively toward interesting applications of Newton’s equations (F=Ma). In

some of these examples, the evolution becomes surprisingly difficult to predict (chaotic) or

occasionally produces pictures of great visual appeal. No prior knowledge of computers is

assumed. Weekly readings will be assigned. At the end of the seminar we will work on

producing artistic prints based on computer outputs. This will be done in collaboration

with two great printmakers: Deanne Wortman, program manager of the Nexus program,

and Anita Jung, professor in the Department of Art and Art History.

2

In this first year seminar, the students will learn how to use computers to visualize the

time evolution of simple systems studied by physicists, mathematicians and other scientists.

The ability to visualize changes is a useful skill in many scientific disciplines. We will

demonstrate that it can also be enjoyed for artistic and creative purposes.

We will focus on simple deterministic evolution rules where the initial conditions deter-

mine the future in a unique way. We will start with concrete examples where the changes

are described by simple algebraic equations (for instance, how to calculate the square roots

numerically or model the changes of population over successive years). We will then work

our way progressively toward Newton’s equations (F=Ma) describing springs or pendulums.

In some of these examples, we will realize that the evolution becomes surprisingly difficult

to predict (chaotic) or occasionally produce pictures of great visual appeal.

Our understanding of the laws of physics has generated many practical applications which

are part of everyday’s life. We want to emphasize that it can also be used to generate objects

that can be considered as artistic. This is a unique feature of this first year seminar.

Students will learn to use the computer language Mathematica (available free to UI

students and which can be used for many purposes). No prior knowledge of computers is

assumed. Only high school algebra and trigonometry is needed as a prerequisite. The classes

will be taught in a classroom equipped with computers (room 201 in Van Allen building).

Weekly readings will be assigned. The class will consist of short presentations related to the

readings and practical uses of computers.

At the end of the seminar, we will work on producing artistic prints based on computer

outputs. This will be done in collaboration with two great printmakers: Deanne Wortman,

program manager of the Nexus program, and Anita Jung, professor in the Department of Art

and Art History. The grade will be based on class participation and student’s presentations.

Course Content

Many of the laws of physics are deterministic. Given some initial situation, these laws

determine the evolution in a unique way. For example, Newton’s laws of motion provide

well-know examples of deterministic evolution where calculations agree very well with ex-

periments or observations, and gravitational forces can be held responsible for the planetary

motion with an incredible accuracy. The advent of computers have stimulated the explo-

ration of deterministic evolution and the discovery of examples where small changes in the

initial conditions can have a drastic effect on the sufficiently long term evolution. This

situation is often referred to as chaotic.

The goal of the seminar is to use computers to explore simple examples of deterministic

evolution where chaos can under special circumstances be observed. These numerical exper-

iments sometimes lead to graphs that have been considered as artistic by previous physics

3

students. Some examples are shown above and at the end of this document.

Textbook

The main textbooks is: Chance and Chaos by D. Ruelle, Princeton University Press,

1991. Other references will be provided during the lectures. Students who would like to

study some topics more systematically may consult standard introductory physics textbooks

(Halliday-Resnick, Ohanian....). A very interesting introductory (but not easy) textbook is:

R.P. Feynman, R.B. Leighton and M. Sands, The Feynman Lectures on Physics, 3 Vols.,

1964, Addison-Wesley (available on line). Occasionally, lecture notes or additional reading

material will be provided by the instructor. These notes will be available online.

4

Homework

A reading assignment will be given each week.

Grade

The grade will be based on class participation and short student presentations related to

the readings.

Tentative list of topics

• Seminar content and introduction to Mathematica.

• Simple deterministic rules of evolution : linear transformation and how to calculate

the square root of 2.

• Translations on a circle and stroboscopic motions.

• Chance and probabilities.

• Deterministic evolution with continuous time.

• Ordinary differential equations and Newton’s Laws.

• Periodicity, quasiperiodicity and chaos.

• Systems of oscillators and the double pendulum.

• Student presentations.

• Artistic rendering of classical mechanics computer outputs.

5

Picture Gallery