MathGroup Archive 2012

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Visualizations of homeomorphism of a square

Letting S be the unit square, I want to find a way of visualizing a
homeomorphism, say f, of it. For example, assume f:S->S is defined
f(x,y)=(x^2,y^2). One way to give a student an idea of what this
function does is to draw a picture of say a circle or a rabbit in the
unit square, and then see what happens under the image of f.

I am hoping to find a way to get mathematica to draw both the preimage
and image. Any help would be greatly appreciated.



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