The Prickly Pear is a fairly unique purple fruit as its texture and location is shared by no other fruits. The texture of the Prickly Pear looks similar to those of the Leaves and can be found on Cacti. When it is grown on a Plant Box, The Prickly Pear will grow as it is Cacti, resulting in you both getting Prickly Pears and Cactus Bits.
You can find this fruit on Desert Island near the small pond. These fruits also appear on Cacti (when grown normally or in a Plant Box.)