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:




Barnes and Noble


Adviva LLC


A1 Books


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)

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 Intrduction, Cambridge University Press, 1990



General Chaos Web Sites





Fractal Generators



Logistic Map





Lorenz Attractor



Mandelbrot Set Generator

Guide to the Mandelbrot Set



Fractal Basin Boundaries



Cellular Automata

Wolfram Mathworld

Logic Gates


Turing Machines


Finite State Machines


Neural Networks - Hopfield Model




Cluster Growth: Dimension d = 2 Random Site Percolation




Cluster Growth: Diffusion Limited Aggregation in d = 2




Cluster Growth: Random Walk


Forest Fire Model

Small World Networks: Agent-Based Models


Artificial Life







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 -
Should be a paper of 5 pages or longer 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.


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