As described here under the section "The "false" Floyd-Steinberg filter":
Much better results would be obtained by using an alternating, or
serpentine, raster scan: processing the first line left-to-right, the next
line right-to-left, and so on (reversing the filter pattern appropriately).
Serpentine scanning –which can be used with any of the error-diffusion
filters detailed here– introduces an additional perturbation which
contributes more randomness to the resultant halftone.
As described here under the section "The "false" Floyd-Steinberg filter":
(Apparently this is also known as Boustrophedon transform dithering.)