Math. The number of combinations grows extremely quickly when you add more options. There are more ways to sort a regular poker deck than there are atoms in the universe.
Even if you make simplifying assumptions and call fingerprints the same when they just share a similar structure you’ll easily end up with billions of possible fingerprints.
If you look at the details more closely (the so-called minutiae, stuff like where exactly one of the line splits into multiples) there are more possible fingerprints than there are possible DNA Strings, practically infinite infinite depending on your measurement precision.
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