Using geometeric series to get different shapes

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We have this final project for my math class and I was thinking of using geometeric series to get different shapes. I found this great website http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/series/serapp.html but our teacher has already used it as an example. Do you know any other easy shapes I could do. Not involving :-p complex numbers...Julia Mandelbrot formula. It doesn't have to be about geometeric series it could be any thing that involves calculus.
 
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You could do the anti-snowflake.
http://math.rice.edu/~lanius/frac/anti.html
 
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