Tradescantia are fast trailing plants grown for striped foliage in purple, silver, green and pink. They grow quickly enough to fill a hanging basket in a single season.
What every Tradescantia wants
Bright, indirect light. This is the one thing that matters. The colour is light-dependent, and in a dim spot the purple fades to plain green and the stems stretch out with wide gaps between leaves.
Water when the top few centimetres are dry. They are thirstier than they look because they grow so fast.
Expect to restart it
Tradescantia go bare and straggly at the base after a year or so. This is normal and not a care failure.
The fix is to take cuttings from the healthy ends, root them in water within a week or two, and start again. Most people keep the same plant going indefinitely this way.
The sap can irritate skin, and the plants are mildly toxic to cats and dogs.