I know this post is old, but that IS a [email protected]
The popular name for this category of lichen is, "false pixie cup" or "pixie cup" or sometimes "fairy cup" lichens. They come in many different species and typically grow in shadier locations, on a log, in gravel (I've found them in landscaped gravel beds next to roads and you wouldn't know they were there unless you were familiar with them).
Lichens are classified into 3 "growing" types, fruticose, crustose, foliose (or in People-Speak: branchy/pokey-looking, flat, leaf-like).
"Pixie Cups" are of the Fruticose type of the genus, Cladonia.
Cheers! from me, the "Bryophyte Babe"
Oh! Forgot to add that the reason you dont see any roots, is because Lichen DONT HAVE ROOTS.
They are not plants, but rather a symbiotic relationship (what I describe as a room & board agreement: you give me a place to live, and in exchange I'll feed you) between THREE ORGANISMS: a fungus, a 2nd fungus more similar to yeast, and an alga. Yes, it used to be thought as only 2 orgs, but latest research shows many are 3.
How do they 'Grow' without roots? They absorb everything they need to grow from the air and from sunlight. How this happens I may need to describe in another thread someday. ;)
Here's a pic I took of one of my favorite lichens