A new arrangement on an old idea

Perhaps you have seen a proof that the cardinality of the set of fractions is the same as that of the natural numbers. It relies on creating an ordered list of all the fractions. If you can talk about the nth fraction, then there must be as many as there are natural numbers.

If you order the fractions and arrange them in the following way, you get a Pascal's triangle - like deal with just as many patterns and interesting features.