Another quicky: Bryce renders using single precision reals. These use 16 bits to represent a value from about 3 x 10^-38 to 3 x 10^38. So there are 16 bits to represent each primary colour, which adds up to 48 bits. If exported when the render has finished, you can save the full range of 48 bits. Otherwise, they are reduced to 8 bits integer values. And here, dithering comes in.
There are indeed many different dithering patterns and Bryce uses one of them. Since a lot of fine details in a transition from one to another colour are lost when reducing to 8 bits, dithering attempts to hide part of the steps. Just like a printer. Look at a print out with a magnifying glass. Just as David said, use 48-bit dithering if you intend to save your renders as a conventional BMP. If you intend to export it as 48 or 96 bits image for later processing, do switch it off, because it introduces a pattern that renders the image useless.
We have to be careful to understand what is meant with those bits. A conventional BMP (or JPG, or PNG) has 24 bits, 8 for each primary colour. A 32-bit BMP has still only 8 bits per colour, plus a fourth 8 bit channel that holds the alpha map.
48 bit TIFF has 16 bits per primary colour (single precision real) and a 96 bits TIFF (or HDR) has 32 bits per colour (double precision reals) - and GeoTIFFs use quad precision reals (64 bits) to represent greyscales with a very fine resolution.