Physics - Geology 30:  Fractals, Chaos and Complexity

Course Syllabus - Winter Quarter, 2018

Lecture Times:  MWF  1:10 - 2:00 pm

Lecture Room:  1348 EPS Building

 

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 pm MW or by appointment


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

http://www.amazon.com/Chaos-Under-Control-Science-Complexity/dp/0716724294/ref=sr_1_1?ie=UTF8&s=books&qid=1195085929&sr=1-1 

 

Barnes and Noble

http://search.barnesandnoble.com/booksearch/isbninquiry.asp?r=1&ean=9780716724292

 

 

Highly Recommended Text

 

Manfred Schroeder, Fractals, Chaos, Power Laws, Minutes from an Infinite Paradise, WH Freeman, New York, 1991.

Available from Amazon

http://www.amazon.com/Fractals-Chaos-Power-Laws-Infinite/dp/0716723573/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1199738780&sr=1-1

 

Optional Text

David Feldman, Introduction to Chaos and Fractals, Oxford, 2012

Richard Kautz, Chaos, The Science of Predictable Random Motion, Oxford University Press, 2011

Other Optional Texts

Briggs, J., Fractals, the Patterns of Chaos, Discovering a New Aesthetic of Art, Science, and Nature,
Simon and Schuster, New York, 1992.

 

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 Introduction, Cambridge University Press, 1990

 

P.S. Addison, Fractals and Chaos, An Illustrated Course, Institute of Physics, Bristol, UK, 1997


(And FYI) New Offering: Master's Degree in Complexity Science

https://santafe.edu/news-center/news/sfi-and-asu-offer-online-ms-complexity

 


General Chaos Web Sites

(On a Mac, many of these JAVA applets can only be run with Safari)


David Peak's Web Site

Frame_Home_Page

Ginger Booth Fractal Java Applets

Game_of_Life

Fractint

George-Shelburne_Webs

http://hypertextbook.com/chaos/

http://www.egwald.ca/nonlineardynamics/logisticsmapchaos.php

UIUC Sites
 

Fractal Generators

http://www.math.umass.edu/~mconnors/fractal/gen.html

http://classes.yale.edu/fractals/

http://en.wikipedia.org/wiki/Fractal

 

http://www.chaospro.de/

 

 

Logistic Map

http://www.geom.uiuc.edu/~math5337/ds/applets/burbanks/Logistic.html

http://math.la.asu.edu/~chaos/logistic_bifurcation.html

http://brain.cc.kogakuin.ac.jp/~kanamaru/Chaos/e/Logits/

 

 

Lorenz Attractor

http://www.cmp.caltech.edu/~mcc/chaos_new/Lorenz.html

 

 

Mandelbrot Set Generator

 

http://www.wackerart.de/fractal_english.html

Guide to the Mandelbrot Set

 

 

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.cs.swan.ac.uk/~csandy/research/play/ca/

http://math.hws.edu/eck/js/edge-of-chaos/CA.html


Wolfram Mathworld

 

Logic Gates

http://wps.aw.com/aw_brookshear_compsci_8/18/4742/1214158.cw/content/index.html

 

Turing Machines

http://morphett.info/turing/turing.html

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

https://cs.stanford.edu/people/karpathy/convnetjs/

http://playground.tensorflow.org

http://facstaff.cbu.edu/~pong/ai/hopfield/hopfieldapplet.html


Probability

http://onlinestatbook.com/stat_sim/

http://www.rossmanchance.com/applets/OneProp/OneProp.htm

 

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


http://apricot.polyu.edu.hk/~lam/dla/dla.html

 

 

 

Cluster Growth: Random Walk

 

http://dananne.org/dart/randomwalk/web/randomwalk.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://www.eddaardvark.co.uk/svg/forest/forest.html


 

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 --   55%            

                                                                                                  3.     Homework  and labs --   25%.           

 

Late Homework will be accepted (within reason)

 

 

Class Project

 

1-paragraph description of the project -
Should be a paper of 3-5 pages researching some topic in chaos/complexity/fractals, preferably involving some computer calculation/graphics, demonstrating and understanding of the basic scientific ideas. It can also be an application to a real system.

IMPORTANT NOTE!! Please refer to the paper style guidelines here.
Note that the paper (Final Project) grade will be based BOTH on style and content.

 

Examples of projects 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 such as generating 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