Implementing the runtime operation in a PLC wouldn't be too bit a deal, just a matter of sequencing a bit array to the valve outputs. Picture a roll going through a player piano. The actual code involved is almost trivial. The real work is getting that graphic into the array.
Now for some numbers. A rough measurement on screen puts the waterfall about 80 droplets (bits) wide, or five 16-point discrete output modules driving the valves. Let's call the line rate 20 Hz (50 msec) and the cycle time 8 minutes, for a total of 9600 lines (20 lines/sec * 60 sec/min * 8 min) and and array size of 48000 words. Just about any PLC/PAC with at least 64K memory and a flat address space (notable exceptions: A-B PLC-5 and SLC-500) can meet the scan time.
Finally, we have to get the graphic into the controller. My thought is that the artist creates it as a monochrome bitmap, 80 pixels wide X 9600 pixels high. A custom program then reads the bmp file and writes each row to the controller array in reverse order. Remember, the waterfall is effectively scrolling down so the graphic has to be sent to the valves from the bottom up. With engough memory, the controller could store several graphics and schedule them for everyday use, special events, holidays, etc.
I leave the heavy mechanical lifting to someone else, especially finding suitable small, fast and long-lived soleoid valves.
