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> positions are encoded as strings over the alphabet on 2 bits

This is the most pedantic way of saying "binary 2-tuples" I've ever seen. Also for quadtrees this is inferior to base 4 because you can assume clockwise (or counter) ordering.

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I don't think that's what they meant. It's the case you can use literal strings of bits to encode a (2^n)-tree node, so you use actual bitstring comparisons and operations to manipulate them. Rightshift gives you the parent and things like that.

I don't think this is something the article cares about, though.

Thank you, that is exactly what I meant.

Uh, base 4 is exactly what I meant. I guess I wasn't very clear that I mean positions are encoded as bitstrings, with one pair of bits for each level (and triples of bits for octrees). Is that clear enough for you?

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