The white pincushion or pincushion (Chaenactis artemisiifolia) is a member of the sunflower family.
It is found from Southern California down into northern Baja, California.
They are very small, so small that I had a difficult time getting a focused picture the first time I saw them near Carey's Castle on April 3rd, in the southern portion of Joshua Tree National Park. Only my side shots turned out. I just went back up to Hayfield Rd today, May 1st, and found some other pincusions, all in a very small area, west of where I have been walking previously. This time I used my Canon SLR camera to photograph them which is better able to focus on small objects than my small digital point and shoot. I was able to get better topside flower photos.
Until taking the photos today and enlarging them, I could not tell that the flower head appears to be many tiny individual flowers. It is difficult to appreciate their beauty until you are able to zoom in and see them close up. That is true with many of the small desert wild flowers.