Just my 2 cents' worth with respect to the screen saver
proposals: how about the following?
1) (This is along the lines of the popular "swarm of
bees" screensaver) Have some bee (or other - perhaps
allow the user to choose from a menu) icons move around
the user's computer screen according to simple dynamical
rules, e.g. allowing them to avoid collisions and
treating the window edges as either reflecting or
periodic boundaries. Every time an LL iteration
completes, use the bottom X ( X is a small integer )
bits of the interim LL residue, treated as a signed
quantity, to set the x-acceleration of widget #1, and
the next X bits for the y-acceleration. Widget #2 would
similarly use the next 2X bits, etc. We use the bits to
set the acceleration rather than the speed to keep the
movements from being too herky-jerky. We'd need to make
sure the computations involved are sufficiently simple
so as not to steal too much runtime from the actual LL
test.
We could also combine the above with some way of
tracking the progress of the current assignment. For
instance, if the number being tested is 2^p - 1 and the
user's screen has N pixels, then on average every p/n
iterations, block one more pixel of the imaginary bee
box, say in inward-spiraling fashion. As the test
proceeds, the walls of the box slowly close in.
(Admittedly, not a good screen saver for the
claustrophobic :)
2) For the folks who like something that looks more
scientific, we could have a vertical box that looks
like a control panel. Every iteration, the bottom Y
bits of the LL residue get printed to the bottom line
of the panel, and the others move up. We could colorize
the individual digits of the hex residues, or pick a
new color for each new Residue, so things look a bit
more dynamic. The faster the user's machine, the more
dynamic the output.
-Ernst
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