The Floyd Steinberg error diffusion dithering algorithm can use a boustrophedonous scan order to eliminate the diagonal geometric artifacts you get by scanning each row the same direction.

https://en.wikipedia.org/wiki/Floyd%E2%80%93Steinberg_dither...

"In some implementations, the horizontal direction of scan alternates between lines; this is called "serpentine scanning" or boustrophedon transform dithering."

I implemented some eight bit cellular automata heat diffusion rules with error diffusion, which accumulated an unfortunate drift up and to the right because of the scan order.

Rudy Rucker pointed out the problem:

http://donhopkins.com/mediawiki/index.php/CAM6_Simulator

"Rudy Rucker: I feel like you might have some kind of bug in your update code, an off-by-one thing or a problem with the buffer flipping. My reason is that I see persistent upward drift in the action, like if I mouse drag a blob it generally moves up. Also the patterns appearing in the blob aren't uniform. I mean...this IS supposed to be the 2D Rug rule, isn't it?"

So instead of scanning back and forth boustrophedoniously (which wouldn't eliminate the vertical drift, just the horizontal drift), I rotated the direction of scanning 90 degrees each frame ("spinning scan") to spread the drift out evenly in all directions over time.

https://github.com/SimHacker/CAM6/blob/master/javascript/CAM...

    // Rotate the direction of scanning 90 degrees every step,
    // to cancel out the dithering artifacts that would cause the
    // heat to drift up and to the right.

That totally canceled out the unwanted drifting and geometric dithering artifacts! That made it possible to cultivate much more subtle (or not-so-subtle) effects, like dynamically switching per-cell between different anisotropic convolution kernels (see the "Twistier Marble" rule for an extreme example).

http://donhopkins.com/home/CAM6