CS382:Chaos templated

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<Chaos>

Overview

This unit is about chaos. Chaos theory describes the behavior of certain dynamical systems, that is, systems whose states evolve with time, that may exhibit dynamics that are highly sensitive to initial conditions. As a result of this sensitivity, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic.

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, and fluid dynamics. Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and weather/climate.

An early pioneer of chaotic theory was Edward Lorenz. Lorenz was using a simple digital computer, a Royal McBee LGP-30, to run his weather simulation. To his surprise the weather that the machine began to predict was completely different from the weather calculated before even though he entered rounded 3 digit number like 0.506 which is close to original 6 digit number like 0.506127. Lorenz had discovered that small changes in initial conditions produced large changes in the long term outcome.

Background Reading for Teachers and TAs

• James Gleick "Chaos: Making a New Science"
  • This book focuses as much on the scientists studying chaos as on the chaos itself.
  • Chapter 1 include the story about Edward Lorenz.
  • There is a copy in science library.

Reading Assignments for Students

• Chaos Theory: A Brief Introduction
  • A brief introduction to chaos theory.
  • This article starts from the story of Edward Lorenz.
• The Lorenz Attractor in 3D
  • Some source codes for rendering Lorenz Attractor.
  • This would be used for lab activity.

Reference Material

• Global Climate Change: NASA's Eyes on the Earth
• NOAA Global Warming Frequently Asked Questions

Lecture Notes

• Lecture 1:
  • Story of Edward Lorenz
  • How he found butterfly effect
  • Introducing the weather model which Lorenz used

• Lecture 2:
  • Climate model
  • Introducing NetLogo-like climate model
  • Basic of earth science (showing the relationship among temperature, pressure, wind, and humidity)

• Lecture 3:
  • Numerical weather prediction
  • Introducing how weather channel forecasts tomorrow's climate
  • Different between numerical weather prediction and deterministic climate model

• Lecture 4:
  • Global warming
  • Can computer scientist predict climate 100 years later?
  • Super computer for climate model (earth simulator, etc)

Lab

• John Conway's Game of Life lab
  • This is a simple example of chaos behavior. Depending on the initial position of cells, they repeat death and birth uniquely.
  • Students can play with this game easily and see how those cells change their form.
• Lorenz attractor lab
  • Students compute Lorenz attractor, obtain values, and visualize the shape.
  • It is possible to implement Lorenz attractor in second life.
• Numerical weather prediction lab
  • Students statistically predict the weather next day/week by using our weather database.
  • Students get weather data on that date in the last 5 years and guess how it will be this year.
  • Some knowledge of database is needed to dive into weather database.

Software

• Game of life(java applet)
• Lorenz attractor in 3D
  • The c source code generates values in 3 dimensional coordinate.
  • Students can generate infinite patterns of values by changing 3 parameters in 3 non-linear differential equations.
  • The values can be plotted with GNUplot like this picture.
  • There is the source code of Lorenz attractor for second life, but it includes numbers of bugs.

Bill of Materials

N/A

Evaluation

CRS Questions

• The butterfly effect is summed up in the title "does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" What does it refer to?
  • a. Pandemonium principle
  • b. The film from New Line Cinema
  • c. Chaos theory
  • d. Tip of insect collecting

• Who found butterfly effect?
  • a. Edward Lorenz
  • b. Hendrik Lorentz
  • c. Edward Teller
  • d. Edward VIII

• What is the chance of rain tomorrow?
  • a. 30%
  • b. 40%
  • c. 50%
  • d. (from weather channel)

Quiz Questions

• Explain why numerical weather forecasts miss their expectation.
• Describe how we can develop deterministic climate model.

Chaos Metadata

• To learn that it's next to impossible to predict the future since it's too much complicated.
• To abstract chaos behavior and understand the mechanism.

Scheduling

Late in semester.

Concepts and Techniques

• Selecting from infinite numbers of parameters for climate model.
• Realizing simple-looks situation causes chaos behavior.
• Transforming data to knowledge by visualizing.

General Education Alignment

• Analytical Reasoning Requirement
  • Abstract Reasoning - From the [Catalog Description] Courses qualifying for credit in Abstract Reasoning typically share these characteristics:
    • They focus substantially on properties of classes of abstract models and operations that apply to them.
      • Yes.
    • They provide experience in generalizing from specific instances to appropriate classes of abstract models.
      • Yes.
    • They provide experience in solving concrete problems by a process of abstraction and manipulation at the abstract level. Typically this experience is provided by word problems which require students to formalize real-world problems in abstract terms, to solve them with techniques that apply at that abstract level, and to convert the solutions back into concrete results.
      • No.
  • Quantitative Reasoning - From the [Catalog Description] General Education courses in Quantitative Reasoning foster students' abilities to generate, interpret and evaluate quantitative information. In particular, Quantitative Reasoning courses help students develop abilities in such areas as:
    • Using and interpreting formulas, graphs and tables.
      • Yes.
    • Representing mathematical ideas symbolically, graphically, numerically and verbally.
      • Yes.
    • Using mathematical and statistical ideas to solve problems in a variety of contexts.
      • Yes.
    • Using simple models such as linear dependence, exponential growth or decay, or normal distribution.
      • No.
    • Understanding basic statistical ideas such as averages, variability and probability.
      • Yes.
    • Making estimates and checking the reasonableness of answers.
      • Yes.
    • Recognizing the limitations of mathematical and statistical methods.
      • Yes.
• Scientific Inquiry Requirement - From the [Catalog Description] Scientific inquiry:
  • Develops students' understanding of the natural world.
    • Yes.
  • Strengthens students' knowledge of the scientific way of knowing — the use of systematic observation and experimentation to develop theories and test hypotheses.
    • No.
  • Emphasizes and provides first-hand experience with both theoretical analysis and the collection of empirical data.
    • No.

Scaffolded Learning

The source code of Lorenz Attractor for second life has bugs. If students fix the bugs and modify by themselves, it would be a practice of coding and understanding chaos behavior.

Inquiry Based Learning

Some prose.

link to old version

To Do

• Fitz is going to try to see if he can get the Lorenz equations to work in Second Life
• Mikio is going to try to finish the rest of it, assuming that Second Life simulation will work at this point