Physics - Geology 30

Fractals, Chaos and Complexity

Winter Quarter, 2020

John Rundle

Professor of Physics and Geology

At Left:  A Map of the Internet


Course Syllabus

Get Adobe Acrobat Reader


Please note that homework can be turned into Professor Rundle either in class, or at his office in 534B Physics-Geology by 5:00 pm on the due date.

Note:  The material in the book by Schoeder is more advanced, and is provided
for students who want to further explore the topics

The material in the book by Feldman covers many of the same topics but is optional.



Reading Assignment


Homework/Lab Assignment

Homework Due Date

1 January 6

Introduction - Exploring Fractals and Chaos

Peak & Frame

Chapter 1, pg 5-17


Chapter 1, 1-25

Course Flyer

The Santa Fe Institute

Overview of Complexity

SFI Big Questions

Pattern Shells

Patterns in Game of Life

Dow Jones Industrials

Parkfield Earthquake Prediction

Climate Change

Jennifer Dunne on Interactions

Geoff West on Cities-I

Geoff West on Cities-II

Duncan Watts on Common Sense and Complex Systems

Forecasting Disasters

Video Feedback: Setting it Up

Video Feedback 1

Video Feedback 2

Video Feedback Crutchfield

Explore Frame Web Site

Frame Web Site:

1 - 1D

Homework: Write a paragraph about your previous experience with fractals and chaos

Friday January 10

2  January 13

Fractals - Fractal Generators & Iterated Function Sets

Intro to Probability

Peak & Frame

Chapter 1, pg 18-40


Chapter 1, 25-49

Optional: Feldman Chapters 14-15

Scaling Laws 

Fractal Antennas

Problems 1


Wednesday Jan 22
3 January 20 Fractals - Cont.

Fractal Dimensions

Peak & Frame

Chapter 2, All

Begin Chapter 3


Chapter 9

Optional: Feldman Chapter 17

Sierpinski Tetrahedron


Fourier Transforms

Hilbert Curve

Fractal Patterns

Fractals Wikipedia

Bruce Malamuds Talk

4 January 27

Fractals, Power Laws, Introduction to Chaos

Peak & Frame

Chapter 3, All

Begin Chapter 4



Chapter 3

Chapter 10, 211-225

Optional: Feldman Chapter 18

Market Probabilities

Rundle Research

Synchronization of Metronomes

 Problems 2  Wednesday Feb 5
5 February 3 Chaos

Iterated Maps
Logistic & Tent Maps
Attractors & Fixed Points

Peak and Frame

Chapter 4, 5


Schroeder Chapter 12

pp 268-286

pp 89-294

Optional: Feldman Chapters 1-7  

Atmospheric Modes

Lorenz Equations

Lorenz Attractor - I

Lorenz Attractor - II

Lorenz Equation Math

NY Times Article:
"In Natures Casino"

Logistic Map View of Current US Trade Policy

Problems 3 Wednesday Feb 12
6 February 10

Complex Fractals Mandelbrot Set


Fractal Boundaries

Newton's Method


Peak and Frame

Chapter 7
Chapter 8


Chapter 11, 237-245

Chapter 12, 295-299

Optional: Feldman Chapters 20-22

M Set Introduction

M Set: Wikipedia

M Set Morphology

Tour of M Set

M Set and Fibonacci Numbers

Julia Set Morphology

Filled Julia Set

Fractal Basin Boundaries

Problems 4

+ 1-paragraph description of project - see syllabus for some examples of possible projects

Friday Feb 21

Due Friday Feb 21

7 February 17

Cellular Automata

Artificial Life

Theory of Computation


Peak and Frame
Chapter 9

Schroeder Chapter 17, 371-386

Optional: Feldman Chapters 23-25

Fractal Stock Prices

Cellular Automata (Wikipedia)


Problems 5

Friday February 28

8 February 24  

Theory of Computation (cont.)

Neural Networks




Chapter 10, 232-236

Optional: Feldman
Chapters 26-27

SFI Complexity Course

Dan Shiffman on Nature of Code

Daniel Shiffman on CAs I

Dan Shiffman on CAs II

Dan Shiffman on Game of Life

Computation in CAs


Conferences on CAs

Alan Turing

Turing Test

Finite State Machines

NY Times Article on AI

Brittany Wenger on Neural Networks

Neural Networks (Wikipedia)

Deep Learning (Wikipedia)

Hopfield on Spiking Neurons


Problems 6

Guidelines for Paper

Friday March 6
9 March 2

Information Theory


Cluster Growth


Pattern Formation

Information (Intro)

Information (Bits)

Information (Entropy)

Probability (Wikipedia)

Probability (StatTrek)

Example: Monte Hall Problem

Example: Secretary Problem

Example: 100 Prisoners Problem


10 March 9

Data Science

Gambling (as a Form of Applied Probability)

Financial Forecasting

Options Trading

Examples and Applications

Suzy Moat on Big Data

Jim Simons on Quant Investing

NY Times Article on Investing Strategy: Buy at the Close, Sell on the Open

Cities and Sustainability

Conflict as Computation

History and Inevitability

Summary & Discussion

Course Projects Due by 5:00 pm Monday March 16

Please hand in all outstanding work by Friday March 13