In other words, the most realistic way would be to use a real 3D application to crate a rolled-up strip that unrolls itself. There may not be any carpet tutorials. but I’ve seen a “scroll” tutorial somewhere.
However, you might be able to fake it in AE with three ingredients:
1: the flat strip of carpet, masked to reveal itself over time
2: the cylindrical roll, created with the CC cylinder effect, with its position and diameter animated as it rolls along.
3: the side of the roll, which would be a shrinking circular disk with a sort of spiral pattern on it. The shrinking should probably be a shrinking mask.
If you can line those guys up and make it work, great. The trick will be working with the cylinder.
But you know … even this cheat would be easier in a real 3D app. 🙂