They're probably Orbeez, but that doesn't answer all the question.
Last week, two Tucson residents headed out to the desert to do some photography. In a remote corner of the desert, they found a huge pile of strange purple orbs. The orbs were puddled together in a single spot, not scattered around as you might expect if they had fallen from the sky. Upon examination, they found that the orbs were squishy and watery. Although most were purple, some were translucent.
The couple sent photographs to a local news station, which headed out to examine the orbs themselves. The reporters described the objects as being "like gooey marbles that ooze out a watery substance when squished."
When contacted, various researchers speculated that they could be a slime mold, amphibian eggs, or some kind of jelly fungus. These natural phenomena have all been observed and recorded many times, although never in the middle of the Arizona desert. Molds, amphibians, and fungi all tend to do better in an environment that is a lot more damp than the Sonoran Desert.
However, members of the public have contacted the station to identify the objects as Deco Beads, a product that is small spheres filled with water used in planters to keep plants watered. Florists have piped up to say that they are hydrogel beads used in floral displays. And still more people (particularly parents of young children) believe that the objects are Orbeez, a toy that seems (to a skeptical eye) to be the same thing as Deco Beads but more expensive, in a wider variety of colors, and marketed to children as a toy.
All of these items are examples of hydrogels, which are a fascinating product in and of themselves. Hydrogels consist of polymer chains that absorb water and trap the molecules between their fibers. Some hydrogels (like those used in the Always Infinity sanitary pad) are designed to never release their fluid load. Others (like those in Deco Beads and floral beads) are designed to slowly release the water over a period of up to a week.
Of course, none of these explanations covers what the objects are doing in the desert. Why would someone drive so far just to dump a bunch of either Deco Beads or Orbeez? Why not just throw them in the trash? Was someone hoping to dehydrate them, in order to rehydrate them later?
Personally I'm going to stick with my all-purpose explanation for every weird, nonsensical thing that some random stranger does: "probably a meth addict."