The plasma effect, for example, uses vertex shaders to calculate in the order of 8 sines per pixel, and then adds some squares and square roots.

Originally, for a plasma effect, one would calculate a sine based value only for each row and each column. For a 320x240 pixel effect, only 320+240 "complicated" calculations were necessary per frame. To combine these at the pixel level, simple adds and bit shifts were enough. This was necessary, because it was entirely impossible to do so many calculations (or even memory lookups) per pixel on old hardware.

The actual effect is nice, but it has little to do with the old demoscene effect :)