I rather like the idea of a tile puzzle where each bit is perfectly square, but care is taken to ensure each bit is also clearly unique in terms of the colors or shapes on it. No edge piece advantage at all.
If the tiles are small enough and the picture big enough, each tile could be a separate picture,
with an average color that decides its position in the puzzle.
Those pictures might help clue you in to where that bit goes, or they might not. The pictures could be ideograms or icons which assemble to form sentences or logical statements and the box would have a crossword puzzle like list of clues.
e.g. "At 21 from left, 7 down, for 5 tiles. Bertrand de Jouvenel quote: 'A society of sheep....' "
and the matching tiles would be:
1. the words "must in"
2. a picture of a clock face
3. the words "beget a"
4. a picture of the capitol building
5. a picture of wolves
All of which are in colors that happen to make up that row of pixels in the over all picture. This row might be generally white with the clock face, capitol and white wolves.
It might even be possible to use the same set of tiles to build more than one picture.
I assume actually designing the puzzle would be pure hell, but that's what makes it half baked, eh? "The proof is left as an exercise for the student."