Way cool, Margaret! It looks like some of the spore are germinating right where they formed. Talk about good humidity! Platyceriums aren't real easy to grow froms spores, even when you're trying!
Ferns alternate generations, and spores grow into gametophytes (prothalli) that look quite different from adult sporophytes (regular, typical ferns we're used to seeing.) They stay small and flat, and each individual prothallus is generally less than a quarter of an inch across. As you can guess, the gametophyte generation has the gametes (messing with these tiny plants is how we get hybridized ferns). After fertilization, the gametophytes will die as (hopefully) the sporophytes root and grow. If your plant stays moist, fertilization might occur in the gametophytes on your plant's fronds, but there wouldn't be enough substrate to support a growing sporophyte. If you want more ferns, you could carefully remove the little buggers and put them in some sphagnum. Otherwise it wouldn't hurt anything to leave them in place as a temporary curiosity.

Alternatively, it's not impossible some spores from a liverwort or another fern have settled in & grown among the Platycerium's spores. I'd think it was more likely the fern's own offspring, though.

Ah Jen, my darlin' little fountain of good information, lol, I knew I could count on you! Thanks so much for a beautiful explanation, I'd love to know not only where you find the time to learn this stuff but also how you find the time to maintain that fabulous collection, be so generous here and still have anything like a real life.

It could be staghorn gametophytes(gotta use this somewhere, use it or lose it, you know, lol), but who knows? My cinnamon ferns and royal ferns don't seem very aggressive(I've heard that they can be but never seen them reproduce even one new plant), the only "wild" fern that spreads around close by has gametophytes(see? I really do need to use these words or I'll never remember them, that's the kind of girl I am) that are very different looking, deep dark green and kind of "carpet-like", I'll post a couple of pictures, one of the fronds and one of the gametophytes(!) and see if you know what it is. There aren't any live oaks nearby with the resurrection ferns in them so I don't think it's that.

I guess I won't ask for any cultural tips, this old monster is almost too big to move around much anymore and it has a white butterfly ginger growing out the side that's been there for a couple of years, poor thing, I thought I liberated it last spring but it's ba-a-a-a-ack!

Thanks again, Jen, you're a Minnesota peach.