What is the answer to this Bongard problem?

Source: Bongard problem #112 by Douglas R. Hofstadter

I’ve scoured the internet, and I’ve yet to find an answer to this puzzle.
(edit: It has been given the title of "Hardest Bongard Problem" presented on like 50 sites, without solution)

In a Bongard problem, you are given 12 pictures, 6 on one page and 6 on the other. The pictures on the left page conform to a rule, and the pictures on the right page conform to a different rule. Furthermore, a picture on one side cannot conform to the rule on the other side. The goal is to determine the rules.

You can find plenty of examples here: http://www.foundalis.com/res/bps/bpidx.htm