I can identify these beauties as a species of Fringe Lily, or Thysanotus.
Most the guides I have looked at show them on graceful stems, or as a trailing climber, while our flowers seemed to be growing at ground level. When I took this photo, I intended to come back the next day and look more closely at the leaves and take some measurements. However, they were gone. For this reason, I am leaning toward the flowers being the Common Fringe Lily (Common Fringe-lily (Thysanotus tuberosus subsp. tuberosus R. Br.) which has flowers that only open for a single day.
It is possible that they are the Twining Fringe-lily (Twining Fringe-lily Thysanotus patersonii R. Br.) with the stems trailing along the ground rather than upward.
The violet and purple flowers were about 2 to 3 cm across and did not appear to have a stem longer than 1 or 2 cm – the lobes of the flower appeared to be resting on the ground, or merely a few millimeters above it. Along with the two I photographed, I noted three or four other examples, all low growing, at various points along the edge of the sand bank that forms the dam wall.