Dynamical Grapher for Quadratic Maps

by Hunter Basselet, Adam Case, and Daniel Jackson


This page is intended to distribute our dynamical graphing Java applet to teachers and researchers interested in plane dynamical systems.

Our applet draws the images of up to 6 families of parametric plane curves under iteration by up to 4 families of quadratic rational self-maps of the plane. It allows for orbit tracing, parameter adjustment, parameter parsing, as well as function composition. This applet is a useful tool for drawing dynamical pictures for quadratic maps of the plane as well as iterated function systems whose functions are quadratic or linear.

Dr. Daniel Jackson has used this program as a teaching aid in a variety of undergraduate courses at the University of Maine at Farmington, ranging from freshmen level "Introduction to Mathematics" to senior level "Fractal Geometry." The grapher may also be used as a research tool for studying the dynamical variation in families of functions.


Dynamical Grapher: Official Release 1.0


A good place to start is with our galleries of examples:
  • Gallery I contains some examples and downloadable save files.
Details on using the Dynamical Grapher are contained in our tutorials and quick guide:

Tutorial #1 - Some Basic Features
Tutorial #2 - Parameter Adjusters and the Discontinuous Graphing Option
Tutorial #3 - User Defined Function Composition
Tutorial #4 - Probabilistic Function Composition
Tutorial #5 - Parameter Parsing
Quick Guide - Summaries of Features
Tips/Tricks - Trouble Shooting

Here are 3 computer labs for use in a classroom setting:

Lab #1 - Fractals and Iteration: The Henon Attractor (.doc) (.pdf)    Lab1.waa
              This lab is designed to be used in an introductory level course.

Lab #2 - Parametric Curves: Make a Halloween Mask! (.doc) (.pdf)
               
This lab is designed to be used in an introductory level course.

Lab #3 - Iterated Function Systems: 2 Examples (.doc) (.pdf)
               This lab is designed to be used in an intermediate level course.

*The authors Basselet and Case were supported by a UMF Michael D. Wilson Scholarship for undergraduate research during a portion of the time this applet was in development. Both gentlemen would like to acknowledge this generous funding..