|Name||User name||Web Page|
To login to your Bridge folder, connect using Finder-> Go-> Connect to Server...-> bridge.sewanee.edu, then select bridge, enter username and password . This will put a "Bridge" icon in the computer's desktop, double -click on it to open it.
Very important: After you are done, log-out from the server by dragging the bridge icon to the Trash.
WEEK 1 TEAMS
|TEAM 1||TEAM 2||TEAM 3||TEAM 4|
Homework for Tuesday night (6/20) (one per team):
1) Find the general equation that predicts how many moves are required for n disks in the Tower of Hanoi game.
2) Use it to calculate the time it would take to complete a game with n = 25 disks, at a rate of 1 move per second. Is it longer or shorter than the average human lifetime (lets say 75 years)?
3) Use it to calculate the time it would take to complete a game with n = 64 disks, at a rate of 1 move per second. Is it longer or shorter than the accepted age of the universe (about 15 billion years)?
4) The 3 points, 1/2 distance chaos game rules produce the Sierpinski Gasket we saw in class. What is your prediction (emerging pattern) for a 4 points, 1/2 distance game (imagine using the corners of a square instead of a triangle)?
5) Read the chapter "A Geometry of Nature" (pages 81-118) of Gleick's Chaos and answer (type them in MS Word) the questions posted at:
Homework for Thursday night (6/22) (one per team):
1) Create the fractal letters of your name and take a picture of your fractal name to be used in your web page.
2) Develop a procedure to always win in the Chaos game.
3) Write the full report on the Fractal Dimension of Paper Balls Lab.
4) Work on the Mandelbrot Set exercise handout.
WEEK 2 TEAMS
| TEAM 1
| TEAM 5
Homework for Monday night (6/26)
1) Individual work: LIFE AND NONLINEAR DYNAMICS
Write a story of your own. Specifically, take an instance from your life where a small choice, perhaps made in an offhand fashion, led eventually to a significant difference in your life. For your parable to be apt to the context of this course, the train of events flowing from your choice has to be deterministic. Try to identify some of the nonlinearities in the "dynamics of your life" that helped cause your choice to initiate the chain of events it did.
To emphasize the magnitude of the effect of this small choice, construct a plausible scenario of the result of your making a different small choice (under the same "life dynamics").
Finally, save your story as HTML using MS Word under the name "Story.html" in your bridge06 folder, and link it from your personal web page.
2) Individual work: Place your name in fractals letters in your personal web page.
3) (one per team) Read the chapter "Life Ups and Downs" (pages 57-80) of Gleick's Chaos and answer (type them in MS Word) the questions posted at:
4) (one per team) The Game of Life (Transition Rules: Birth if surrounded by 3 live cells ("mother, father and midwife"), Survival if surrounded by 2 or 3 live cells, Death otherwise)
a) Determine by hand the next generation of the Life configurations below
b) Determine by hand the next two generations of the Life configurations below
Using LifeLab and the random initial condition, observe which stable configurations arise spontaneously from the Life rules.
(Allow some time to pass before drawing any conclusions - the transients must be allowed to die down.).
Indicate what gliders (stable patterns that propagate through the system) did you find.
Homework for Wednesday night (6/28)
1) (Individual Work) Some deep philosophical questions:
"Human consciousness, free will, or feelings can never be understood in terms of physical laws."
"People are mechanistic entities whose behaviors emerge from the same principles that govern all forms of matter."
Here are two opposite views of humanity.
Construct an argument that supports each position.
Which argument do you find more compelling?
Post your arguments as "Discussion.html" and link it from your personal web page.
2) Find the slope (dimension D) from the plot of Mass vs Diameter for the DLA growth process. Make sure you run the applet long enough to have several data points.
3) (one per team) Read the chapter "The Butterfly Effect" (pages 9-31) of Gleick's Chaos and answer (type them in MS Word) the questions posted at: