Ceramic tile - how random are "random" patterns?

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Is there a technical specification for ceramic tile that tells whether each tile had a different random design versus whether there are a limited number of random-looking, but identical tiles?

In the past few months, I've seen different types of ceramic floor tile installed in several rooms of a house. In several of the rooms, the patterns on the tiles are random-looking, but close inspection shows there are identical tiles - not just similar tiles, but tiles that are as identical as two prints of the same photograph. It makes me wonder about the technology that's used to create the patterns. Perhaps the colors are put on by something like an ink jet printer.
 
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For many decades a company in the UK sold a "random" pattern tile that actually used a repeating pattern. The tiles were/are square so rotating them increased the apparent randomness of the pattern by a factor of 4.

Unfortunately one of the tiles has a shape that looks a bit like duck although people don't notice until it's pointed out. Once someone has told you about the duck you can't avoid seeing it whenever you visit someone's house that has this brand of tile. You can also tell if the person who did the tiling knows about "the duck".
 
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