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