Make a binary tree listing all matrix products of
1 0 and 1 1
1 1 0 1
If you multiply
1
1
on the left by all these matrices, you get the Calkin-Wilf tree. If you multiply
1 1
on the right by these matrices, you get the Stern-Brocot tree!
math.colorado.edu/~kstange/pap...
