My friend Alida said: They're very pretty, but I do suggest your compost needs more nitrogenous material so bacteria grow as well. This seems to have too much carbohydrate in it. Add manures if you can, or fresh green waste. And turn it.
I said no to the manure. A couple of inches below these beautiful things is a couple of inches of horse manure. I did say yes to the turning. Will see to that.
My friend, Denis, of The Nature of Robertson has identified the fungi for me. The elegant black and white mushrooms are Coprinus calyptratus. The small white hooded ones are the young of the species.