Arduino with using Adafruit NeoPixel library set one color, fade random pixels in strip on and off
You simply have to treat each pixel individually.


Pick a pixel
Add it to a fade list
Fade all the pixels in the list by a step
Remove pixels which are below some threshold
Repeat


How you do those things like picking the pixel is up to you. You'll probably want to brighten some as well, using a similar algorithm.