Image:Foldings2.png
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Pre-images of the areas from the square domain of the horseshoe that remain in the square.
Produced with Postscript and Illustrator
[edit] Notes
The square on the left gets mapped by the Smale Horseshoe map to the green region. Successive iterations will fold the original square even more. Only part of the original square gets mapped back into the square.
The solid orange part indicates the points in the square that get mapped back into the square by one iteration (for the left square) or two iterations (for the right square).
The original points of the square also get oriented in different directions. The dashed regions in orange indicate how to continue the orientation of the orange strips. No points in the dashed orange region participate in the dynamics of the horseshoe.
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- (del) (cur) 15:38, 21 May 2005 . . XaosBits (Talk | contribs) . . 2048×1276 (46,739 bytes)
- (del) (rev) 04:08, 31 March 2005 . . XaosBits (Talk | contribs) . . 2048×1276 (46,599 bytes)
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