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Visualizations of homeomorphism of a square

• To: mathgroup at smc.vnet.net
• Subject: [mg126267] Visualizations of homeomorphism of a square
• From: Andrew Clifford <andykabandilly2 at gmail.com>
• Date: Sat, 28 Apr 2012 05:24:05 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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.

Thanks,

Andrew