I took four strips and attached them to a power supply at 5 volts. Everything worked great! I did notice, however, that they start off synchronized with the same random seed, which means that they're displaying the same drips even when they shouldn't. I'm going to have to fix that.
I will also have to come up with a solution for the wire. Something that will be waterproof and permanent.
I still need to put in the code to adjust the brightness with a button press.