The right modifier:

Experimenting with different, unique ways of using modifiers can yield interesting and extremely useful results. I encourage you to try and find other ways of making features do things they were not designed for. A bend modifier, for example, if "rolled-up" to an overlapping cylinder can scoop up geometry into a roll.

The procedure:

1. Create a flat Box, 24+ segments for it's longest axis, add a Bend modifier and set it to bend the long axis of the Box
2. Crank up the bend Angle to about 1500 and set Limit Effect on, with the Upper Limit: at about twice the length of your 'carpet' object. (It is easier to visualize the effect if you increase to these settings by spinner  - use the Ctrl key for acceleration.)
3. Enter Sub-Object mode and move the Gizmo along the carpet's length axis.

This can be used on any geometry, though it only works well when it's relatively flat.

A bit more realistic:

More experimentation reveals a solution to the overlap problem. If you rotate the bend mod's Gizmo (in SO mode) along the axis parallel to the "roll", but still move the Gizmo along the carpet's length axis, it will effectively skew the roll effect and force the geometry inward. (Note: You may need to use Transform Type In to get less than a 0.5 degree rotation for this to just slightly skew the geometry. - In the figure to the right the effect is exaggerated.)

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