> 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.
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.
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?
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.