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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.
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..
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