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On Aug 19, 2:47 pm, socraticquest <socraticqu...@xxxxxxxxxxx> wrote:
> Hello,
>
> Any recommendations for software that simulates Henri Poincare's
> 'geometric operation of stretching?' Is there software available that
> can run on Windows XP, and allows users to input there own images to
> simulate Poincare's experiment?
>
> Thank-you
See the article with pictures here:
http://cse.ucdavis.edu/~chaos/courses/ncaso/Readings/Chaos_SciAm1986/Chaos_SciAm1986.html
I saw a talk once where this simulation was done - but it was not
real.
It could be made real if you use a computer algebra program.
Here is what it would do:
1. Find a matrix that when taken to some power n, return to the
original matrix.
2. Use this matrix to represent vectors on the a 2-d screen.
3. Take a graphic that (x,y) coordinates on the screen and multiply
and plot them.
You should be able to simulate the images in the cited reference above
(I actually did it - but only used simple images and Mathematica a
long time ago).
The talk was called "The order within chaos" by Chris Rorres.
I think he even had it in the book: Elementary Linear Algebra:
Applications Version by Anton and Rorres (from Drexel University).
HTH ~A
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