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8 Summary
All of the facts discussed in this paper may be discovered experimentally
by students using a personal computer. The Mandelbrot
Set Explorer is a tool designed to accomplish this. While proofs of
many of these facts are well beyond the typical high school or undergraduate
student, we have nevertheless found that these concepts serve to pique
the students' interest in mathematics. Students first marvel that the counting
or adding phenomenon is true. Soon they begin to wonder why it is true.
It is our feeling that this is the beginning of a wonderful mathematical
experience for the students, one that is very rarely enjoyed in the standard
curriculum.
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