I wanted to add this to the database and *believe* it to be Beavertail Cactus (Opuntia basilaris) but since I'm not a desert person, thought I would get confirmation (or correction). This was taken in the Joshua Tree Park in late January of this year. Thanks.

It is typical of the prickly pear cactus for the Joshua Tree Park, does not have thorns but he has Glochidie, fine hairs are dangerous. She says blindsman - cegador , for the risk of the introduction of glochidie into the eye for grazing freely animals.
looks like quilted cushion.

According to what I could find, Opuntia basilaris is the only Opuntia species native the Mojave Desert that doesn't have spines. So, yes, it's almost certainly Opuntia basilaris.

Thanks. I will add to database. Wish I would have kept the plant pamphlets they kept giving me...but too much paper while traveling.