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Name: Diane A.
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Question:
I would like to be able to explain to my geometry students why fractals such as Sierpinski's triangle and the Mandelbrot Set are both fractals, yet they appear so different and although they are both generated by an iterative process, the processes seem to be different. Can you give me a formal unifying definition of fractals?



Replies:
There are two ideas you have to get to gain a sense of what fractals are all about: "self similarity", and "fractal dimension." Self similarity is pretty apparent: if you see some feature in a fractal, you can always look more closely and see that same feature--or something very like it-- on a smaller scale. Fractal dimension is a harder idea to get. Here are two explanations from the web:

http://math.bu.edu/DYSYS/chaos-game/node6.html

http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html

Tim Mooney



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