@b4c50e1b @2c8b8664 Thanks for the explanation!  It's beautiful even before the amazing diagram.  Something confuses me about the diagram: it would make more sense to my eyes if the labels "64/729" and "729/64" swapped places.  All arrows except the two arrows to and from these nodes multiply by 3/2. The arrow from 729/64 to 32/243 multiplies by 2/3, as does the arrow from 243/32 to 64/729.

(And especially sorry if I am "that guy".)