Physics - Geology 30

Fractals, Chaos and Complexity

Winter Quarter, 2024

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 and 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

 Atmospheric Modes

Lorenz Equations (Wikipedia)

Lorenz Equations: Sensitive Dependence

NY Times Article:
"In Natures Casino"

M Set Morphology

Julia Set Morphology

Fractal Basin Boundaries

M Set: Wikipedia

Logistic Map Explorable with Widgets

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

Logistic Map - Mandelbrot Set Video (18:38)

Benoit Mandelbrot TED Talk (17:09)

Holly Krieger on M Set Introduction (9:10)

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)

Holly Krieger on Filled Julia Set (6:47)

Newton's Fractal (26:05)

Julia & Fatou Sets, Holomorphic Dynamics (27:42)

4 January 24

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 (6:40)

Systems Theory of Organizations (10:53)

Synchronization of Metronomes (4:00)

Veritasium: Synchronization (20:57)

Met Office: Global Climate System (3:51)

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)

PBS on Chaos and Weather Prediction (6:13)

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 Series (8:24)

Introduction to Time Series Analysis (2:59)

Introduction to Fourier Transforms (20:56)

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

Fourier Transforms (Technical)

Basic Probability (7:50)

Independent and Dependent Events (6:43)

Probability Densities (9:36)

Simple Introduction to Probability (11:28)

Simple Introduction to Statistics (4:49)

Histograms and Other Charts (7:34)

Mean, Mode, Standard Deviation (7:34)

6 February 7

Physics of Computation and Information



Peak and Frame

Chapter 7
Chapter 8


Chapter 11, 237-245

Chapter 12, 295-299

Optional: Feldman Chapters 20-22

Alan Turing

Turing Test

Finite State Machines (Wikipedia)

Video on Turing and Turing Machines (13:04)

Making of the Film "The Imitation Game" (14:15)

Best Scenes from the Film "The Imitation Game" (6:05)

Turing Machines (4:21)

A Real Turing Machine (5:08)

Information (Intro 3:25)

Information (Bits 9:52)

Information (Entropy 7:04)

Understanding Shannon Entropy (12:07)

Introduction to Information Theory (10:09)

Information (Markov Chains 7:14)

Information (Statistical Communication Theory 4:01)

7 February 14

Cellular Automata, Neural Networks and Machine Learning


Peak and Frame
Chapter 9

Schroeder Chapter 17, 371-386

Optional: Feldman Chapters 23-25

Cellular Automata (Wikipedia)

Computation in CAs (Melanie Mitchell)

MitchellCAsandGAs (Melanie Mitchell)

Dan Shiffman on Nature of Code (E-Book)

A New Kind of Science (E-Book)

A New Kind of Finance (Paper)

Introduction to Machine Learning

Future of Data Science Education

(CAS) General Overview of CAs (7:51)

Daniel Shiffman on CAs I (6:02)

Dan Shiffman on CAs II (19:39)

Dan Shiffman on Game of Life (16:03)

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)

Google Cloud Tech: What is Machine Learning? (5:22)

Google Cloud Tech: The 7 Steps of Machine Learning (10:35)

Google Cloud Tech: Plain and Simple Estimators (Involves some coding; 5:46)

StatQuest - Neural Network Fundamentals Part I - Inside the Black Box (18:53)

Statquest - Neural Network Fundamentals Part II - Backpropagation (17:33)

StatQuest - Machine Learning Fundamentals: Bias and Variance (6:35)

Deep Learning in 6 Minutes (5:51)

Deep Learning: Structure, and What is a Neural Network? (19:13)

Deep Learning: How Machines Learn (21:00)

Deep Learning: Backpropagation (13:53)

What is Artificial Intelligence (or Machine Learning)? (6:14)

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

What is a Fitness Landscape? (10:15)

Predicting Protein Folding with AI (7:54)

Revolutionizing Protein Folding with AI (12:06)

Self-Organized Criticality (SOC: 10:01)

Applications of Percolation Models in Finance (8:10)

Network Dynamics (6:47)

Network Robustness (18:32)

Diffusion Limited Aggregation (3:04)

Is the Gulf Stream Collapsing? (13:32)

What if Gulf Stream Shut Down?

Lecture on Slowing Down of Gulf Stream, by Dr. Stefan Rahmstorf (U. Potsdam, 27:00, includes movie clips from Day After Tomorrow - start at 12:00)

9 February 28

Cryptocurrencies and Econophysics

Fractal Patterns in Stock Prices

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

Buy Bitcoin Web Site

Tradeblock Web Site

Coindesk Web Site

99Bitcoins The Role of Money, and What Led to Bitcoin? (12:48)

99Bitcoins Bitcoin Mining (16:00)

99Bitcoins Bitcoin Block Confirmations (2:02)

99Bitcoins What is a Hash? (1:53)

What is Bitcoin? History of Bitcoin (12:10)

A Brief History of Bitcoin (5:03)

How Bitcoin Works in 5 minutes (5:25)

How Cryptocurrency ACTUALLY works (13:54)

Bitcoin: How Cryptocurrencies Work (9:25)

How does a blockchain work - Simply Explained (5:59)

CNBC: Wall Street Adoption (12:50)

Valuing Bitcoin - Panel Discussion Crypto 2022 (31:35)

CNBC: President Biden's New Crypto Order (11:29)

Suzy Moat on Big Data (15:54)

Jim Simons on Quant Investing (23:07)


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

Neil Howe: The Fourth Turning: Why American 'Crisis' May Last Until 2030 (14:42)

Neil Howe: The 4th Turning (8:03)

PATREON: We Are In A "FOURTH TURNING," What Does That Mean? (10:20)

The Fourth Turning - How this crisis was predicted 30 years ago (10:04)

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