I have a lot of moss like "steppable" growing across the broken slate area under our pergola way in the back. I'll hazard a guess and say it's Irish moss. It's spread so much that you can no longer see the slate pieces anymore in most areas. It can be lifted up like a mat of carpet so I was going to take a utility knife and cut it all back to where it will just be overhanging the edges of the cracks between each piece of slate. However rather than toss all those pieces out in the compost will they root elsewhere or do you need to get some of the actual "root" that grows in the soil between the stones? A couple of my neighbors are clamoring for some and I have lots to give.