How many zoom levels are enough?

While processing the GBIF data index for all species to display the maps shown in the last post I though it worth showing the number of "occurrences per species per cell" at the various zoom levels.
We make use of the tiling mechanism employed by many mapping clients, who request 256x256 pixel tiles and then we process the data to be several zoom levels ahead of the one displayed.  It is really quite simple, and best described with a couple of examples. 

Processing to 4 zoom levels ahead looks like:

Processing to 6 zoom levels ahead looks like:

When processing to 6 zoom levels, the following shows where it becomes unnecessary to process anymore (around zoom level 11):