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E.g. https://en.m.wikipedia.org/wiki/Hilbert_curve

Any permutation could be used, but I suppose you'd want to use ones that form some sort of visually recognisable pattern. For example, a spiral emerging from the centre of the image, or all the even numbered pixels from a linear scan followed by all those indexed by an odd number.

"a spiral emerging from the centre of the image"

Would this be middle-out compression?

Polar coordinates?

Z-order (aka Morton order) is widely used in GPU acceleration, as a means of converting 2D locality into 1D locality.

https://en.wikipedia.org/wiki/Z-order_curve