Dynamical Systems
The Linear Model
--given by this recursion rule:
Pn+1 = RPn + K
Dynamical Systems, Worksheet 1 homework
Dynamical Systems, Worksheet 2 classwork
Dynamical Systems, Worksheet 3 homework
Dynamical Systems, Worksheet 4 computer lab
Dynamical Systems, Worksheet 5 web diagrams
Dynamical Systems, Worksheet 6 homework
Dynamical Systems, Worksheet 7 special case of R = -1
Dynamical Systems, Worksheet 8
The Logistic Model
--given by this recursion rule:
Pn+1 = aPn(1 - bPn)
Dynamical Systems, Worksheet 9 classwork on escape sets
Dynamical Systems, Worksheet 10 computer lab
Dynamical Systems, Worksheet 11 web diagrams
Dynamical Systems, Worksheet 12 using algebra
Dynamical Systems, Worksheet 13 understanding the bifurcation diagram
Dynamical Systems, Worksheet 14 classwork connecting linear systems to logistic model
Stability versus Sensitivity classwork
Sea of Chaos computer lab
http://johnbanks.maths.latrobe.edu.au/Chaos/index.html--web site that provides an illustrated definition of chaos
Applications of Recursion
Introduction to the Game of Life homework
Game of Life Computer Lab computer lab
Game of Life Applet to play the Game of Life
Hensel's Life Page includes another applet for playing Life, along with lots of interesting Life patterns
Paul's Life Page lots of information about Life
Brian Eno's talk on generative music--from InMotion Magazine
Managing Medication classwork
Disney World Debt classwork
Complex Dynamics
Julia Set Maker--use it to create black and white images to include in your portfolio paper
What are those pretty pictures?QR Students explain it all!
Introduction to Julia Sets computer lab
High Resolution Julia Sets computer lab
Fractint Home Page--download Fractint to make your own Julia Sets at home
http://math.bu.edu/DYSYS/--web site from Boston University--good general information about the logistic model and Julia images
http://skal.planet-d.net/quat/f_gal.ang.html--Dynamical Systems with Quaternions (4-dimensional numbers)
http://astronomy.swin.edu.au/~pbourke/fractals/quatjulia/--Quaternion Julia Sets
http://www.lboro.ac.uk/departments/ma/gallery/quat/index.html--more on dynamical systems with quaternions
Applet to see pendulum in phase space