Random blue eggs… Do chickens have a monthly cycle beyond the daily egg?

I bought four chicks last June to add more egg color to my basket and they started laying consistently around December. I got two marans for dark eggs, an olive egger, and a cream legbar. The marans check out, their eggs are really dark, sometimes speckled, and sometimes have a bloom that makes them look kind of rosy. The one labeled olive egger seems to be laying light brown eggs, which I knew could happen but still, sad. My cream legbar is missing some typical legbar traits and I am pretty sure she is the one laying green eggs, so I am guessing she is actually a mix, basically just another olive egger type.

But here is the weird part. Over the last 7 weeks and 5 days I have gotten three blue eggs. The first was January 29, then February 27, and the most recent yesterday March 23. At first I thought maybe my cream legbar was finally starting to lay and would give me blue eggs, but now it is just this random occasional blue egg. What is causing that, is it some kind of laying cycle thing?