Irish moss (sometimes called Scotch moss) forms a tight mound like moss does, and it works well as a ground cover around stepping-stones and in rockeries. Irish moss thrives in zones 6 to 9.

• Irish moss or Scotch moss (sagina subulata) is a moss-like groundcover with small white summer flowers. It is ideal for rock gardens, but can be a grass substitute for some sites. It does best in rich, well-drained acid soils, according to Ellis, and is hardy in zones 5 to 9. Be sure to find the sagina species, as several other plants are also often sold as Scotch or Irish moss.

• Moss campion (silene acaulis) is a common wildflower in the high European and North American alpine tundra, but it can also be purchased and grown between paving stones in the higher reaches of zones 3 to 5. It grows in small mounds about 2 inches tall, and has a profusion of tiny flowers for a brief period in the summer.  

 

• Moss pink or creeping phlox (phlox subulate) or creeping phlox is another good option for garden paths and rock gardens. It forms a mossy carpet, but has plenty of spring flowers. Unlike true moss, it thrives in dry, sunny soil and does not tolerate much trampling, according to Diane Relf of Virginia Cooperative Extension. A variety of phlox cultivars are available and hardy in zones 3 to 8.

Moss and its sound-alike alternatives are good ground covers for rock gardens and shady or difficult turf grass sites.

Source: http://www.networx.com/article/moss-ground-covers

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