What are the conditions for cactus to grow in Terraria?

The wiki now lists the following four requirements for Cacti to grow:

• There needs to be at least a 1 thick layer of sand below it.
• The Cactus requires 1 space of open ground to either side. A raised tile will block growth, but a lower tile will not.
• The sand it grows on needs to be above the ground level.
• They only grow in the inner 3/4th of the map.

You can't plant cactus but all it needs is sand.

Here is a bit of an instructional vid from Youtube.