<== 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 accessible 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): We [Kaplansky and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury. — Irving Kaplansky (1917-2006), quoted in John H. Ewing and F.W. Gehring, ed., Paul Halmos: Celebrating 50 Years of Mathematics, Springer, 1991.
The complete list of quotes is available here.