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<== This is a picture from the interactive geometry
package Cinderella showing the behavior of 10,000 starting
values in the rectangle [0,1]x[h-1,h+1], where h is the height of the
horizontal line, after six iterations of the algorithm which reflects
a point x in the sphere then reflects the outcome in the line and then
averages the result y with x. It is an accesible prototype for a
remarkable image reconstruction algorithm known variously as
Douglas-Ratchford, Lion-Mercier, Fienup's method, and
"divide-and-concur." Some related graphics can be generated and
displayed at these URLs:
Expansion
Reflection
(wait 30-60 seconds to see the display).
Quote of the day (refresh browser to select another):
The only way of discovering the limits of the possible is to venture a little way past them into the impossible. -- Arthur C. Clarke, "Hazards of Prophecy: The Failure of Imagination", in his book Profiles of the Future, 1962. See also Wikipedia article.
The complete list of quotes is available
here.
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