Purple sea urchins, like most sea urchins, are herbivores. They primarily eat algae.

Here's a breakdown of their diet:

* Macroalgae: They graze on large, visible algae like kelp, sea lettuce, and other seaweed species.

* Microalgae: They also consume tiny, single-celled algae called phytoplankton, which they filter from the water.

* Detritus: They might eat small amounts of dead plant and animal matter that falls to the seafloor.

The exact species of algae that a purple sea urchin eats will depend on its location and the availability of food. However, their diet is largely focused on consuming algae to sustain themselves.