On Fri, 09 Feb 2001 17:56:26 EST, you wrote:
>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.
My hunch is that this wouldn't steal much time if the bees move by
jumping rather than sliding.
>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 :)
The thing here is that this would make the rate of progress slow. I
know that when I first started GIMPS, I got a little depresseed
thinking things like "I've been here an hour and it's not even a third
of a percent done!"
There are possible ways to make it appear that work is being done
quickly- the Tower of Hanoi comes to mind, though we would need to
make double moves on some iterations, since runtimes can only be a
power of two steps.
Perhaps there could be an option to play a fanfare or some such every
time one of the six or seven bottom discs in the tower is moved.
>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.
That's also a fairly interesting idea.
Maybe the colorization could vary with the current iteration number in
some fashion - for example, we could have the lines of text each
broken into blocks of rainbow color, with each column of blocks
shifting according to the base 7 number of the current iteration - it
would start partway through, according to how far below the next
highest power of 7 the exponent was.
Then, as the run continued, the right-hand word in each line would
shift by one color for each iteration, wrapping around - when the
bottom line was solid violet, you'd be done.
Nathan
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