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: 23 pm MW or by appointment 
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
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, 2012 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 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/newscenter/news/sfiandasuofferonlinemscomplexity


General Chaos Web Sites (On a Mac, many of these JAVA applets can only be run with Safari) Ginger Booth Fractal Java Applets
Game_of_Life http://www.egwald.ca/nonlineardynamics/logisticsmapchaos.php Fractal Generators
http://www.math.umass.edu/~mconnors/fractal/gen.html
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
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/edgeofchaos/CA.html
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://tamswww.informatik.unihamburg.de/applets/hades/webdemos/45misc/05fsmeditor/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/enotes/Perc/perc.htm
Cluster Growth: Diffusion Limited Aggregation in d = 2
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 

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 selfsimilarity 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 "selforganization" arise in systems with feedback, and the ways in which those processes lead to the emergence of coherent spacetime 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
1paragraph
description of the project 
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
