This math shirt illustrates connections between Number Theory, Combinatorics and Set Theory. The Calkin-Wilf Tree is a binary tree containing each positive rational once. It is related to Euclid's Algorithm and the number of ways of representing an integer as a sum of powers of 2, where each power of 2 is used at most twice.
The descendants of a/b are a/(a+b) and (a+b)/b. These are fractions which would lead to a/b by one step of Euclid's Algorithm.
When read row by row, from left to right, the sequence of fractions has the property that each denominator is the numerator of the next fraction. The sequence of numerators is the number of ways of expressing n as a sum of powers of 2, using each power of 2 at most twice.