Yeah... An Arduino would work to generate pulses to drive a strobe. But, you really don't need
an Arduino. Something like a 555
chip can be used to build a variable pulse generator.
It's going to take more than one LED. So, you'd need a MOSFET (or something) to boost the power of the Arduino (or 555). The trick with a strobe is to light-up the action with the strobe (which takes plenty of light), and then have darkness (so you can't see the movement) between flashes.
The combination of a dark room and flashing lights means that something like this needs a special environment and is not practical for a "living room" decoration.
Or, you can just buy a strobe... Even if I was going to build something, I'd probably buy one to experiment with first.
Here is an LED strobe light
, and here
is a smaller one. A traditional strobe
(or flash) uses a Xenon flash tube. These require a few-hundred volts and are a bit tricky to build.
It's fairly easy to make a spoked-wheel or a fan look-like its stopped or rotating backwards. The water might be trickier... The drops need to be evenly-spaced and approximately equal in size, so that the "next" drop appears
to be the "previous" drop falling upwards. For that, you'll just have to get a pump and some tubing, and experiment!