Is there logic or a pattern to the number of eyes that each Minion has? Is it based on age? Gender? Social status? Something else?
You can answer this question in two ways:
- Plot device
Biology In the opening credit sequence of the Minions Movie we see the minions evolving from single cell organisms. As they rapidly evolve (presumably over time in the real timeline of Minion world) we see that they depict two minions with two eyes and one with a single eye. So to your specific question of
Is there logic or a pattern to the number of eyes that each Minion has? Is it based on age? Gender? Social status?
The answer seems to be NO. Despite contradicting Darwinian Evolutionary Theory, all three Minions go through a series of evolutionary changes - this could just be symbolic of multiple generations of Minions over time. As they "evolve" or transform in the sea they keep following the next villainous sea creature until a Dinosaur leaves the sea and they follow. They have the same two with two eyes and one with one eye.
As they swim up to leave the ocean and follow the Dinosaur, we see a large group of Minions many with the double and single eyes:
So we can really only say that Minions have always been that way - for millions of years if we assume their timeline is the same as our Earth timeline.
The more obvious reason why they have one or two eyes is that it is used as a plot device so that the Minions can be distinct to movie viewers. They are all yellow, wear denim overalls and goggles and speak with very similar voices, so body type, hairstyle and number of eyes seem to be the primary distinguishing characteristics that make one a Kevin and the other a Bob for example.