Actually, I used a small piece of slate and then the carpet kind of spread over the substrate beyond the borders of the slate. Riccia grows pretty quickly!
If you go to Wal-Mart, you can get loofahs (synthetic bath sponges) for $1 or $2 each. Go home and unravel it. It becomes this huge mesh/net thing. I just put some riccia on slate or stainless steel mesh, wrap it with the netting, and tie the netting on the underside of the slate pretty tightly. It'll look ugly until the riccia grows up and covers the netting, but once it does, it looks pretty nice.