Sometimes known as 'mother of thousands', this is an excellent groundcover for shady sites - even full shade (ht 20cm). It is a native of eastern Asia. It has rounded leaves with pretty silver veins and spreads by stolons, though it is never a nuisance. In late October, it sends up petite flower stalks with tiny white blooms, which are like a cloud of miniature moths. It forms an excellent carpet. It needs some moisture to be seen at its best, but has no other requirements and will cope with some dryness. I have found that it will climb up shady walls!
I like to pair it with Arthropodium cirratum, the New Zealand renga renga lily, which flowers at the same time with vaguely similar-shaped blooms. It is also pretty grown with rhizomatous Begonia which have their airy flowers around the same time and also prefer shade; and the Saxifraga has a sort of a Begonia 'look' to it, somehow, which makes them look good together! Propagate from the plantlets that form and root at the tips of the stolons.
In cooler climates such as the Blue Mountains of NSW, I have seen a lovely cultivar with splashes of white and red on the foliage (known as 'Tricolor'), and another with distinct burgundy segments between the leaf veins; I am not sure if they would grow well in Sydney but I hope to try them one day! I have also heard of (but never seen) a golden-leaved version.