Walking the RGB color space using the Hilbert curve is pretty neat! Here's what it looks like using the first 4 Hilbert curves:
@adereth would be interesting to see some images with palettes reindexed to the corresponding nth-order curve's palette!
@cemerick Like this?
ImageCollage[Table[ColorQuantize[chas, RGBColor /@ Rescale[HilbertCurve[i, 3][[1]]]], {i,4}]]
@cemerick @adereth As palettes the adjacency provided by the Hilbert curve disappears, right? So this is just quantizing the RGB components to 1, 2, 3, or 4 bits respectively. Looks like Mathematica's `ColorQuantize` is doing some error-diffusion dithering, I think Floyd–Steinberg though I can't be sure.
Palettes taken from almost-continuous motion along the *n*th-order Hilbert curves (say, 256 or 512 colors along the 2nd-order curve) would be a way of letting the Hilbert nature bleed into the image.
Posterizing to 3 bits per component (quantizing the color without dithering) would also look pretty cool.
@radehi @cemerick You're right, looks like ColorQuantize dithers by default. Here it is with and without dithering: