I mentioned a sky ceiling to a customer's wife and she wants me to look into it. I would rather it be some kind of thin mat with the fibers poking out, so a dark scrim can be installed over it. If it looks like stars twinkling, even better. I really don't want to build one from scratch.

A small projector could work, too- that way, it could look like the Earth is rotating.

Sounds interesting. not sure how that would work... Embed the fibre optics in the mat somehow?

Maybe some sort of LED light array first, then get a mat with holes in it to go under it.... Then you could use some sort of controller to twinkle the LED's....

Hmmm....

I'd be interested to see what you find. I've never seen anything other than tiles....

But if your going to scrim it anyway... Why not tiles?

Tiles have been the popular way to do it for the last several years. Most economical if you are attaching them straight to ceiling. Much more if you have to create a drop ceiling (due to attic space) and lose some height in the room.

The old way of drilling small holes all over the ceiling from the attic and fixing fiber strands with (epoxy, silicon, etc.) back to a controller. Was extremely time consuming = very expensive.
Unless it was for your own place or a friend you were working for free. Then the fiber & light controller are the cheapest way, material wise. Whole kits start at less then $200 for 200 3 sized fiber, with twinkle effect LED light engine [covering about 50 sq.ft. or less].
But if you don't have crawl space above the ceiling, you would still have to build a drop ceiling to do it. Loosing some height in the room and the cost of the new drop ceiling.

The way pico projectors and projection mapping are going ... it'll all be done that way soon.

Level five drywall finish, seal and apply vinyl wrap of the sky and embed the fibers.

I agree with Julie. Here is a discussion of Planetarium technology over the ages.

Sort of related question: How does one repaint a ceiling that includes embedded fibers?

A completely different approach would be to create a light box above the drywall (or whatever), then punch short light pipes through from the finished side of the ceiling.

Kinetics makes 3 options for fiber optic panels.