Entodon seductrix is the top of the list. Entodon seductrix is a pleurocarp that grows on soil, wood, and stone. Other sun tolerant mosses include Climacium americanum, Leucobryum glaucum, Ceratodon purpureus and Bryum argentium. These are listed in order of usefulness for your application. Woodland Gardens, Stones Wall, Water Features, Stones Pathways, Back Yards, Step Stones, Moss Gardens, Growing Moss, Backyards
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"However, I had first to rid myself of encumbrances. Just beyond the drive a low shape rose, which proved to be a poorly maintained privet hedge, vastly overgrown but easily breached. I deposited my boots and the several skirts behind it, tucked the doll into the back waistband of my trousers...and crept across the drive to the wall of the house." --Laurie R. King
Love the checkerboard paving - if you were careful about the 'grass' you planted, you wouldn't need to mow (e.g. microlaena, chamomile, thyme, creeping mint, even violas...) I've always loved this idea, but having to continually maintain it put me off. Love the idea of a ground cover that wouldn't need to be mown
At the bottom of William Wordsworth's garden at Rydal Mount rests this mossy stairway, long forgotten.