Physics - Geology 30: Fractals, Chaos and Complexity Course Syllabus - Winter Quarter, 2014 | |
Lecture Times: MWF 1:10 - 2:00 pm Lecture Hall: 1362 Geology
GEL 30 Section 001 CRN PHY 30 Section 001 CRN |
Instructor: John Rundle, Professor of Physics and Geology Offices: 534B Physics Building 2131 Earth & Planet Sci. Building Office Hours: 2-3 MWF or by appointment |
Required Course Text:
David Peak and Michael Frame, Chaos Under Control, WH Freeman, NY, 1994 Currently out of print, but can be obtained from the following vendors:
Amazon
Barnes and Noble http://search.barnesandnoble.com/booksearch/isbninquiry.asp?r=1&ean=9780716724292
Adviva LLC http://base.google.com/base/a/1362126/D16501640674093539284
A1 Books http://search.a1books.com/cgi-bin/mktSearch?act=showDesc&code=gbase&rel=1&ITEM_CODE=0716724294
Highly Recommended Text
Manfred Schroeder, Fractals, Chaos, Power Laws, Minutes from an Infinite
Paradise, WH Freeman, New York, 1991.
Available from Amazon
Optional Text David Feldman, Introduction to Chaos and Fractals, Oxford, 2010 (Xerox copies can be purchased from JB Rundle) Other Optional Texts
Briggs, J., Fractals, the Patterns of
Chaos, Discovering a New Aesthetic of
Art, Science, and
Nature,
Gleick, J., Chaos, Making a New Science, Viking, New York, 1987.
Waldrop, M.M., Complexity, The Emerging Science at the Edge of Order and Chaos, Simon and Schuster, New York, 1992.
G.L. Baker and J.P. Gollub, Chaotic Dynamics, An Intrduction, Cambridge University Press, 1990
|
|
General Chaos Web Sites
http://hypertextbook.com/chaos/
http://www.egwald.ca/nonlineardynamics/logisticsmapchaos.php Fractal Generators
http://www.math.umass.edu/~mconnors/fractal/gen.html
Logistic Map
http://www.lboro.ac.uk/departments/ma/gallery/doubling/ http://to-campos.planetaclix.pt/fractal/lorenz_eng.html
http://brain.cc.kogakuin.ac.jp/~kanamaru/Chaos/e/Logits/
Preditor-Prey http://www.adam.com.au/therevills/AL%20pp.htm http://www.stensland.net/java/erin.html
Lorenz Attractor http://www.cmp.caltech.edu/~mcc/chaos_new/Lorenz.html
Mandelbrot Set Generator
http://www.coolmath.com/fractals/fractalgenerators/generator1/index.html
http://www.wackerart.de/fractal_english.html
Fractal Basin Boundaries
http://brain.cc.kogakuin.ac.jp/~kanamaru/Chaos/e/Newton/ http://www.personal.psu.edu/faculty/m/x/mxm14/fractal.htm
Cellular Automata http://www-module.cs.york.ac.uk/nstc/applets/CellularAutomata/index1d.html Logic Gates http://wps.aw.com/aw_brookshear_compsci_8/18/4742/1214158.cw/content/index.html http://matwww.ee.tut.fi/ote/year3/gates/
Turing Machines http://www.turing.org.uk/turing/scrapbook/tmjava.html
Finite State Machines http://tams-www.informatik.uni-hamburg.de/applets/hades/webdemos/45-misc/05-fsm-editor/chapter.html
Neural Networks - Hopfield Model http://www.cbu.edu/~pong/ai/hopfield/hopfieldapplet.html
Probability http://bcs.whfreeman.com/ips4e/cat_010/applets/Probability.html http://onlinestatbook.com/stat_sim/
Cluster Growth: Dimension d = 2 Random Site Percolation
http://www.ibiblio.org/e-notes/Perc/perc.htm
Cluster Growth: Diffusion Limited Aggregation in d = 2
Cluster Growth: Random Walk
http://math.furman.edu/~dcs/java/rw.html http://www.math.utah.edu/~carlson/teaching/java/prob/brownianmotion/4/rw.html http://polymer.bu.edu/java/java/1drw/1drwapplet.html
Forest Fire Model http://schuelaw.whitman.edu/JavaApplets/ForestFireApplet/ http://www.eddaardvark.co.uk/fivecell/forest.html Small World Networks: Agent-Based Models http://mcbridme.sba.muohio.edu/ace/labs/
Artificial Life
|
|
Prerequisites
None
|
|
General Comments: This course will introduce students to the ideas of Fractals, Chaos, Complexity and Computation. We will begin with the examples of objects, such as trees, river networks, coastlines, weather, earthquakes, the human body, the stock market, evolution, and others that display examples of fractal geometry. We will then explore many of the fascinating ideas popularized by B. Mandelbrot and others about self-similarity across different geometric scales. Chaos, how it arises in familiar everyday systems, and the link with fractal geometry, will be discussed. We will talk about how processes of "self-organization" arise in systems with feedback, and the ways in which those processes lead to the emergence of coherent space-time structures for systems with no natural length or time scales. We will discuss the idea of Cellular Automata and its relationship to computation. We will examine how chaos and order are inextricably linked with a kind of strange duality. Many of these ideas are having a profound effect in fields far from their point of origin. As a result, we will explore the profound philosophical implications of these ideas, including their effects on modern art and architecture, and especially on the definition of life itself.
| |
Course Content
Topics to be Covered Include:
1. Geometry, self similarity, and patterns 2. Making fractals through recursive iteration 3. Measuring fractals - fractal dimension 4. Chaos, randomness, and noise - similarities and differences 5. Iterated maps - the logistic and tent maps - fixed points 6. Complex numbers and the Mandelbrot set 7. Edge of chaos, fractal boundaries, and fractal domains 8. Cellular automata and information processing 9. Applications to real systems
| |
Homework and Grading:
1. Class Participation -- 20% 2. Final Project -- 65% 3. Homework and labs -- 15%.
Late Homework will be accepted (within reason)
| |
Class Project
1-paragraph
description of the project -
Examples might include 1. A discussion of the fractal nature of river networks, trees, bronchial tubes, or the like. 2. A small project on chaotic maps, such as the logistic map, and how they can be applied to real systems 3. A project on fractal art, how to generate the images, such as trees, mountains, rivers, or other fractal objects 4. An investigation of neural network learning models, and how these can be used in real applications 5. A research project on the theory of computation, and how dynamical systems can carry out computation
|