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one might wonder whether perhaps some other ordering would make it easier to compress more complex images.

One simple approach is just to assemble a large collection of images typical of the ones that one wants to compress, and then to order the basic forms so that those which on average occur with larger weights in this collection appear first. The pictures on the next page show what happens if one does this first with images of cellular automata and then with images of letters. And indeed slightly higher levels of compression are achieved. But whatever ordering is used the fact seems to remain that images that we would normally consider complex still cannot systematically be compressed more than a small amount.

Captions on this page:

Examples of images obtained by keeping only certain fractions of the complete set of basic forms. In the case of both simple and completely random images, many features are recognizable even with fairly few basic forms—implying that a highly compressed representation can be given.

From Stephen Wolfram: A New Kind of Science [citation]