This site contains an interactive applet that allows the user to investigate the Julia sets inside the circle of radius 2.
Type of Material:
This site can be used for demonstrations or for individual student practice.
Identify Major Learning Goals:
Develop a better understanding of discrete dynamical systems and Julia sets in particular.
Target Student Population:
Students in Dynamical System course.
Prerequisite Knowledge or Skills:
Basic knowledge of discrete dynamical systems
This module allows the user to investigate the Julia sets associated with functions f(z) = z^2 + c for any complex number c in the circle of radius 2. After pressing the Draw button, the applet draws a Julia set, where the points are color coded as “prisoners” and “escapees”. This applet can also motivate its user to investigate the Mandelbrot sets.
Although there are tabs for explaining the Julia Set, many students will end up playing with the tool without learning about the mathematics behind the Julia Set.
Potential Effectiveness as a Teaching Tool
The site can be used as a part of in-class demonstration or a self-guided activity. A list of suggested activities with this tool is given under Instructor tab. A set of links to related discussions, lessons, and worksheets makes this module ready to use to any instructor who teaches the subject. The Learner tab also provides a variety of examples that can be done with this applet.
Since Julia Sets are often just an exploration topic rather than a main topic in a course, the student would benefit from having very clear explanations of what a Julia Set is. There is an explanation in the related resource section: Discussion about Prisoners and Escapees—Julia Sets, but a student who goes to the resource without any help from an instructor may end up just playing with the tool and enjoy the beauty of the set without understanding what it does.
Ease of Use for Both Students and Faculty
A user can starting working with this tool right away by changing input parameters and executing the applet. There is a link to instructions explaining how to print output if necessary. There are also instructions for each of the components of the tool.
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