Fractalina and Franimate! are mathematics education software designed to help teach ideas about fractals to high school and middle school students through hands on experimentation and exploration.
Fractalina implements "the chaos game" (technically Iterated Function Systems in which each transformation is affine). By inputing the compression and rotation values, and the position for each of an arbitrary number of transformations the student can specify the IFS, which can then be drawn by pressing the start button. Other features include: zoom, different color modes, preset IFSs, and hidden features which allow the teacher to save a fractal to a gif file, and hide the IFS settings. For a more information see About Fractalina.
Franimate! allows animations of fractals generated using Fractalina. The user specifies a few "key frames" (each a separate Fractalina window) which the animation should go through. The program then generates the animation by linearly interpolating the values of the IFS parameters between key frames. The user can set the number of frames between key frames, the playback speed, and a number of other parameters. For more about Franimate! see About Franimate!.
These pages only include information about the programs, their background, and how to use them. The Dynamical Systems group at B.U. will, at some point, write up materials to help teachers use these programs in their classes.
The author, Noah Goodman, is an undergraduate student in math and physics at the University of Arizona. He has great hopes of getting into graduate school next year and spending several more years avoiding avoiding real life. To find out more about him look at Noah's homepage, or write, he always likes getting email.
Go to the applets: Fractalina, Franimate!.
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