Apologies in advance for the long-winded answer to what looks like a simple question.
>Can a 16x16 image be illegal?
>What about a 64x64 image?
Depends on the case. If you could show the 64x64 image of child abuse to a stranger and they'd go "that's child abuse" (repeat x12 for a jury) then yes.
However, there's another aspect of possession charges that says the suspect has to be aware they're in possession of an illegal image and able to access it. A 64x64 image is problematic, nobody watches anything in 64p so the only time you would see such a small image is thumbnails. If someone has an illegal image in a thumbs.db file, but they have since deleted the original full-sized image, they likely don't know a thumbnail of the image was being kept on their hard drive. And if they don't know how to extract images from the thumbs.db file they're not in possession.
The interesting loophole in UK law is that you can get charged for "creating" indecent images of children. Popular belief is that it means creating new images but it more often than not refers to creating copies. In the case I mentioned, they could still get arrested for creating a 64x64 copy of the illegal image as a thumbnail. And you can usually prove that they knowingly did something that would trigger the creation of the thumbnail (downloaded the image from a dodgy P2P application 99% of the time).
So to answer this:
>What's the situation like if you have two chunks of data (perhaps at two separate locations on the blockchain) and only if you XOR them you get the illegal image?
It's complicated. Mainly because it's hard to tell who the "you" is in this situation.
But assuming someone is accused of downloading both chunks of data, yes it would be illegal if the person involved knew how to XOR them to get the illegal image. The specific term in UK law is "tools or knowledge". So someone with decades of experience in anything compsci might not have to have any programs capable of XORing the two chunks together if the prosecution can prove they had the knowledge to do so using standard OS tools or write their own script/program.
Really XORing is no different than encryption, you've basically just described a one-time pad. And in any cases involving encryption if you can prove that the person possessing encrypted illegal images had either decrypted them in the past, or has the capability to decrypt them (knows the password, has a keyfile, or can bruteforce) then they're legally in possession. If they had XOR'd the two chunks together already there would likely be a copy somewhere in slack space/unallocated sectors and that would be creation. In the end it would come down to a huge number of factors specific to the case.