Physics  Geology 30: Fractals, Chaos and Complexity Course Syllabus  Winter Quarter, 2022  
Lecture Times: TuTh 10:30  11:50 am Lecture Room: 1348 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: By appointment 
Recommended 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 https://www.barnesandnoble.com/w/chaosundercontroldavidpeak/1119266031?ean=9780716724292 AbeBooks https://www.abebooks.com/9780716724292/ChaosUnderControlArtScience0716724294/plp
Manfred Schroeder
(Available from Amazon)
(Available from Amazon)
Optional Texts: 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, Simon and Schuster, 1992 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 Frame_Home_Page (Some links are broken) Wolfram Demo Sites (Includes many types of demos  search for chaos)
Game_of_Life II Logistic Map http://brain.cc.kogakuin.ac.jp/~kanamaru/Chaos/e/Logits/ (.jar file) http://www.egwald.ca/nonlineardynamics/logisticsmapchaos.php http://rocs.huberlin.de/D3/logistic/ Lorenz Attractor (.jar file)
http://math.hws.edu/eck/jsdemo/jsMandelbrot.html Anatomy of the Mandelbrot and Julia Sets Fractal Basin Boundaries http://brain.cc.kogakuin.ac.jp/~kanamaru/Chaos/e/Newton/ (.jar file) http://www.personal.psu.edu/faculty/m/x/mxm14/fractal.htm >
Cellular Automata 1D Cellular Automaton Simulator 1D Cellular Automaton and Edge of Chaos Logic Gates https://en.wikipedia.org/wiki/Logic_gate Turing Machines http://morphett.info/turing/turing.html http://www.turing.org.uk/turing/scrapbook/tmjava.html Neural Networks (Develop Yourself Using Neuroph) https://developer.ibm.com/tutorials/ccartificialneuralnetworksneurophmachinelearning/ Probability and Statistics http://onlinestatbook.com/stat_sim/ (Note JAVA code won't run) http://www.rossmanchance.com/applets/OneProp/OneProp.htm Percolation
Cluster Growth: Dimension d = 2 Random Site Percolation http://www.ibiblio.org/enotes/Perc/perc.htm (JAVA code won't run) Cluster Growth: Diffusion Limited Aggregation in d = 2
Cluster Growth: Random Walk http://dananne.org/dart/randomwalk/web/randomwalk.html https://demonstrations.wolfram.com/search.html?query=random+walk 

Prerequisites
None, although at least 1 term of calculus is highly desirable


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. Cryptocurrencies and Decentralized Finance (DeFi) 10. Complexity and the Climate System 11. A topic in Econophysics 12. Applications to other real systems
 
Homework and Grading:
1. First Paper/Project  50% 2. Second Paper/Project  50% 3. Extra Credit Problems  10%.
Late Papers will be accepted (within reason)
 
Class Project
1paragraph
description of the project  Examples for the first paper/project 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, generating images like trees, mountains, rivers, or other fractals 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 Examples for the second paper/project might
include
1. A discussion of a selforganizing complex system such as the weather, earthquakes, social systems, the world wide web, the economy, the financial markets, biological systems, ecologies, evolution, etc., including emergent coherent structures, spacetime patterns, phases of the system and phase transitions 2. A computer code that addresses some other aspect of complex systems not covered in the course 