In ‘Same Stats, Different Graphs,’ Matjeka & Fitzmaurice show a method for purposefully creating datasets which are identical over a range of statistical properties (of your choosing), yet produce dissimilar graphics. In my mind there’s a connection here to the idea of adversarial inputs to deep neural nets, which we might similarly express on some level as ‘Same Stats, Different Classes.’ Another thing I get from this paper is a very visual reminder of ‘Same Outcome (in terms of stats), Different Causes.’ There are lots of different hypotheses you could come up with that may produce the effect you’re seeing.