Chaotic Dynamics Handouts

• Course Syllabus
• Homework Assignments (1)
• Intro to Matlab Handout
• Handout 1: Matlab scripts for Chapter 3 (In text format)
• Sample script 1
• Sample script 2
• Sample script 3
• Function: D(x)
• Sample script 4
• Experiment 3.6
• Sample: Newton's Method
• Sample: The Tent Map
• Handout 2: Homework for Ch 6
• Matlab Scripts for Chapter 6 (Bifurcations)
  • Example Script: Plot cx-x^3
  • Example Script: Second iterate of cx-x^3
  • Example Script: Fixed/Periodic points, cx-x^3
  • Example Script: Full bifurcation diagram for x^2+c, using initial point x=0
  • Function file: ternary.m Use to get the first n digits of the ternary expansion. Example: y=ternary(0.1,5); produces a vector y holding the first 5 digits of the ternary expansion of 0.1.
• Projects Handout

Fractal Geometry Handouts and Code

• M-file to create Serpinski Gasket (Random Iteration Algorithm
• C code to generate the escape time plot, Serpinski Gasket
• Picture of what the C code generates
• C Code to generate the escape time plot, Pattern 1
• Picture of what the C code generates
• C Code to generate Barnsley's Fern
• Picture of what the C code generates
• M-file to create the word "MATH"
• Handout on Iterated Function Systems **Sorry, only available as compressed postscript (due to the graphics)

Three Body files

• threebody.m This M-file defines the differential equations for the 3-body planar problem.
• bodyscript.m A script file to run a three body planar simulation.

Other scripts and interesting code!

• Miscellaneous Julia set Code in Matlab
1. Julia set 1
2. Julia set 2
3. Julia set 3
4. Julia set 4
• (For Josh W's project) Here is some code written in C to produce the picture of the basins of attraction for a pendulum over three magnets. To run the code, save it as pendulum1.c, compile it (for example, type: gcc -lm pendulum1.c ), then run it by typing: a.out
  The result is a data file stored as: pendulum.dat
  which can be loaded and viewed in Matlab: X=load('pendulum.dat'); then: imagesc(X)
• From Stephen's project on Cubics
  • newton.m
  • julia2.m
  • newtonmovie.m
  • juliamovie.m
  • zoommovie.m
  • birds.m
  • birdscript.m