Course Materials 

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Exams

• Exam I - Review, Sample (PDF)
• Exam II - Review, Sample 1, Sample 2 - Some problems for fun!

Introduction

Do you know what the Butterfly Effect is? Let Ian Malcolm [Jeff Goldblum] explain Chaos theory (from Jurassic Park): - https://www.youtube.com/watch?v=5cVLUPwrSmU

What is Chaos Theory? – “Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. ”

• Fractals in Nature and Mathematics: From Simplicity to Complexity, (2017)
• Butterflies, Ferns, and Fractal Landscapes: The Emergence of Complexity from Simple Systems, (2014)
• Predicting the Future of the Solar System: Nonlinear Dynamics, Chaos and Stability, (2006)
• Card Shuffling as a Dynamical System, (2004)

1D Maps

• Logistic Map
• Cobweb plot, Desmos Plot
• pynamical - Python paper
• Bifurcation Diagram Images
• Tent Map
• Chaotic Maps
• Chaotic Dynamics and Itineraries
• MATLAB 
  • plotlogmap.m
  • bifurf.m - Ex - bifurf(1,4,0,1,200)

2D Maps

• Henon Map
• MATLAB Maps -
  • Henon.m,
  • Gingerbreadman.m, gingermap.m
• ChaosHW2.mws
• Fibonacci.mws

Onset of Chaos

• Lyapunov numbers for logistic map
• Itineraries and Itinerary.mws
• binary to decimal conversion
• Standard Map (and here )
• Magic of Perfect Shuffles - See the paper
• Dr. Herman's Card Shuffle Talk
• Faro Shuffle Tutorial

Fractals

• Chaos Game - MATLAB
• Crumpled paper
• Fractal Software
  • Fractint - old DOS/Windows
  • Fraqtive - open source
  • GNU Xaos - open source
  • Ultra Fractal
  • Mandelbrot set HTML5
  • Wolf Jung's Mandel
  • IFS Construction Kit
• MATLAB Files
  • ifs.m - fern
  • ifsOctave.m - GNU Octave version
  • IFSChaos.m - CHAOS Fractal
  • boxcount.m from File Exchange and boxFig.m
    • stri.jpg
    • fern.jpg
    • FractalTree.jpg
    • fractal_tree.jpg
    • carpet.png

Systems of ODEs

• Duffing Equation -
  • duffing.m, duffingeq.m
  • fduffing.m, fduffeq.m, fduffing2.m
• Homoclinic orbit - homoclinc.m

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Additional Items

• XPPAUT/XPP - system solver
• Dynamical systems Software

ChaosBook.org chapter "Local stability" part 1 of 2 and other video lectures and The Course

Chaos, Fractals, & Dynamical Systems

Crumpled Paper

MATLAB Files

• Deterministic IFS for Triangles tri2.m
• "Chaos" as an IFS IFSChaos.m
• Grid Generator for Block IFS blocks2.m
• A More compact IFS Code MyIFS.m
• Old MATLAB page

Python Files

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