Physics - Geology 30

Fractals, Chaos and Complexity

Winter Quarter, 2022

John Rundle

Professor of Physics and Geology

At Left:  A Map of the Internet


Course Syllabus

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The Lectures are Here.

Textbooks listed in the syllabus are suggested but not required. Note that readings listed below are not required, but students can find much interesting information related to topics in the course. The lecture slides contain many references to URLs where further information can be found, but the lecture slides are intended to be for the most part self-contained.



Suggested Readings


Homework/Lab Assignment

Homework Due Date

1 January 3

Introduction - Exploring Fractals and Chaos

Peak & Frame

Chapter 1, pg 5-17


Chapter 1, 1-25

Course Flyer

The Santa Fe Institute

Pattern Shells

Patterns in Game of Life

Dow Jones Industrials

Treasury Yield Curve

Parkfield Earthquake Prediction

Climate Change

Overview of Complexity (3:34)

Complexity Theory Overview(10:51)

SFI Big Questions (5:06)

SFI: Searching for Order in the Complexity of Evolving Worlds (4:38)

Jennifer Dunne on Interactions (4:40)

SFI: Evolution of Complex Societies (6:00)

SFI: Evolution of Life and Intelligence (7:15)

Geoff West on Cities-I (7:17)

Geoff West on Cities-II (17:33)

Jared Diamond on Why Societies Collapse (19:48)

Duncan Watts on Common Sense and Complex Systems (10:54)

Forecasting Disasters in the Complex Earth (JBR 1:09:25)

Video Feedback: Setting it Up (6:49)

Video Feedback 1 (3:19)

Video Feedback 2 (1:56)

Video Feedback Crutchfield (15:33)

Art Benjamin on Fibonacci Numbers (6:24)

Stock Trading with Fibonacci Numbers (9:33)

What is a Fractal Pattern? (2:00)

Emergence in Complexity Theory (9:12)

Explore the Links on the Syllabus page


Write a paragraph about your previous experience with fractals and chaos

Tuesday January 11

2  January 10

Fractals - Fractal Generators & Iterated Function Sets

Peak & Frame

Chapter 1, pg 18-40


Chapter 1, 25-49

Optional: Feldman Chapters 14-15

Gaussian Normal Statistics

Scaling Laws

Fractal Antennas


The Fractal Explorer Web Site

Chaos_Game (Using Excel)

What is a Fractal? (4:13)

Fun with Fractals (5:04)

BBC: How Fractals can help you Understand the Universe (3:09)

Fractals are Often not Completely Self-Similar (19:54)

Understanding the Universe with Fractals (3:09)

Sierpinski Tetrahedron

Hilbert Curve

Cantor Set

Koch Snowflake

Fractals Wikipedia

How Long are Coastlines?? (6:00)

SFI: Fractal Dimensions I (5:30)

SFI: Fractal Dimensions II (5:30)

SFI: Fractal Dimensions III (2:30)

SFI: Fractal Dimensions IV (7:13)

SFI: Fractal Dimensions V, Box Counting (4:42)

SFI: Fractal Dimensions VI, Box Counting(3:38)

SFI: Fractal Dimensions VII Examples from the real World (3:45)

Numberphile: Measuring Coastlines (8:03)

3 January 17 Fractals - Cont.

Introduction to Chaos and the Mandelbrot Set

Lorenz Equations

Iterated Maps

Attractors & Fixed Points

Logistic & Other Maps

Fractal Boundaries

Newton's Method

Peak & Frame

Chapter 2, All

Begin Chapter 3


Chapter 9

Optional: Feldman Chapter 17

Synchronization of Metronomes (4:00)  

Atmospheric Modes

Lorenz Equations (Wikipedia)

Lorenz Equations Sensitive Dependence

Story of the Lorenz Equations (11:50)

Science of the Butterfly Effect (12:50)

Lorenz Attractor - I (13:21)

Lorenz Attractor - II (1:34)

Jack Wisdom: Chaos in the Solar System (3:33)

Uncertainty in Weather Forecasting

NY Times Article:
"In Natures Casino"

Logistic Map - Mandelbrot Set Video (18:38)

Holly Krieger on M Set Introduction (9:10)

M Set: Wikipedia

M Set Morphology

Tour of M Set (5:11)

Fractals, A World in a Grain of Sand (15:00)

Holly Krieger on M Set and Fibonacci Numbers (9:59)

Julia Set Morphology

Holly Krieger on Filled Julia Set (6:47)

Fractal Basin Boundaries

Logistic Map Explorable with Widgets

4 January 24

Introduction to Dynamical Systems

Atmospheric Modes: Nonlinear Dynamics in the Real World

Peak & Frame

Chapter 3, All

Begin Chapter 4



Chapter 3

Chapter 10, 211-225

Optional: Feldman Chapter 18

Intro to Dynamical Systems (1:53)

Systems Theory of Organizations (10:53)

Met Office: Coriolis Effect (1:53)

Met Office: Coriolis Effect & Winds (6:18)

AU Met: ENSO I (4:15)

Met Office: ENSO II (4:23)

Sengupta: ENSO Walker Circulation (6:19)

Nat GEO: ENSO (2:50)

AU Met: Understanding ENSO (4:13)

Met Office: North Atlantic Oscillation (2:13)

Met Office: Atlantic Multidecadal Oscillation (2:28)

Met Office: Pacific Decadal Oscillation (2:50)

Met Office: North Atlantic Oscillation (2:13)

Au Met: Madden Julian Oscillation (3:45)

United Nations: Milankovich Cycles (6:34)

5 January 31 Time Series and Probability

Peak and Frame

Chapter 4, 5


Schroeder Chapter 12

pp 268-286

pp 89-102

Optional: Feldman Chapters 1-7

Probability (Wikipedia)

Probability (StatTrek)

Example: Monte Hall Problem

Example: Secretary Problem

Example: 100 Prisoners Problem

Market Probabilities

Introduction to Fourier Transforms (20:56)

Fourier Transform, Fourier Series, and Frequency Spectrum (15:44)

Fourier Transforms (Technical)

6 February 7

Introduction to Computation, Information and Cellular Automata



Peak and Frame

Chapter 7
Chapter 8


Chapter 11, 237-245

Chapter 12, 295-299

Optional: Feldman Chapters 20-22

Cellular Automata (Wikipedia)

Dan Shiffman on Nature of Code (E-book)

Daniel Shiffman on CAs I (6:02)

Dan Shiffman on CAs II (19:39)

Dan Shiffman on Game of Life (16:03)

Information (Intro 3:25)

Information (Bits 9:52)

Information (Entropy 7:04)

Information (Markov Chains 7:14)

Information (Statistical Communication Theory 4:01)

Computation in CAs (Melanie Mitchell)

MitchellCAsandGAs (Melanie Mitchell)

7 February 14

Introduction to Neural Networks and Machine Learning


Peak and Frame
Chapter 9

Schroeder Chapter 17, 371-386

Optional: Feldman Chapters 23-25

Alan Turing

Turing Test

Finite State Machines (Wikipedia)

Video on Turing and Turing Machines (13:04)

Making of the Film "The Imitation Game"

NY Times Article on AI

Brittany Wenger on Neural Networks (8:23)

John Hopfield and Neural Networks (3:54)

Hopfield Paper on Spiking Neurons

Neural Networks (Wikipedia)

Deep Learning (Wikipedia)

Deep Learning: Structure (19:13)

Deep Learning: How Machines Learn (21:00)

Introduction to Machine Learning

Future of Data Science Education

First Paper:

On a topic related to low dimensional systems, fractals, chaos, or other topic from the first half of the course:

Due Friday February 18

Guidelines for Paper

Example Paper Format

8 February 21  

Landscapes, Networks, Adaptation, Statistical Models

Cluster Growth


Pattern Formation



Chapter 10, 232-236

Optional: Feldman
Chapters 26-27

SFI Complexity Course

Math of Sandpiles

Percolation Theory (8:10)

Network Dynamics (6:47)

Network Robustness (18:32)

Diffusion Limited Aggregation (3:04)

9 February 28

Introduction to Cryptocurrencies and Econophysics

Suzy Moat on Big Data (15:54)

Jim Simons on Quant Investing (23:07)

Fractal Patterns in Stock Prices

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

What is Bitcoin? (12:48)


10 March 7

Data Science

Global Warming, Prediction in Complex Systems

Examples and Applications

Summary & Discussion

Niel Howe and William Straus on the Fourth Turning

The Fourth Turning

Conflict as Computation (2:29)

History and Inevitability (4:06)

Second Paper/Project due describing and analyzing a high dimensional complex system of your choice,
or other topic related to the second half of the course.

Due by 5:00 pm Monday March 14