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The Smale Horseshoe is the result of an infinite sequence of operations on a unit square. To make it, first, stretch the square by a factor of 3 in the x direction, then compress it by a factor of 3 in the y direction. Then, fold the rectangle and fit it back into the square. Repeating this generates the horseshoe attractor. If one plots a phase space (takes a cross section) of the final structure, it is seen to correspond to a Cantor Set, and therefore it is an example of a system showing order amid chaos. Also, in the final mapping, the proximity of any two points is completly independent of their initial proximity.

A somewhat lacking picture can be found at
http://donar.physik.uni-bremen.de/nlp/publications/ChaosHTML/r14richter/node4.html (although lacking, you can see the beginings of the cantor set forming)

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