Arduino Controlled LED "Aircraft Runway" lights? Answered

Excuse me Please:

I have a project with a specific need, which I "think" an Arduino and LED strips can meet.
The effect I would like is to have the LEDs all dimly lit, and have a single/few run along the length of the strip with increased brightness and returning to the dim intensity once past.
think: aircraft runway lights.
also, which I think may overly complicate the project, I need like ten strips all running concurrently, each with singular/few brighter LEDs running the length and randomly repeating.
does what I explain make sense?