Now you've got me curious what the compression ratio would be if you just re-ordered an image's pixels using a Hilbert curve (so that in e.g. a 100x100 image, the first 100px scanline contains the first 100px of the Hilbert path through the original image) before passing it to PNG for compression.
• Lenna.png (http://i.imgur.com/pPNbiyG.png): 475KB.
• Lenna.Hilbertized.png (http://i.imgur.com/kU8C3yG.png): 709KB.
Clearly, not a good idea, at least for photographic sources.
In this case, PNG's filtering makes it kind of 2D-aware, so that probably works better on the original. But if you tried splitting it into 8x8 blocks, then predicting each one from the left-upperleft-upper neighbors, well, you'd have the basics to modern DCT codecs.
https://upload.wikimedia.org/wikipedia/commons/8/89/PNG-Grad...