interactive ambient light setup question

Hello all. I have an idea about building an interactive ambient lighting system to be mounted on my ceiling. Here is a basic sketch of the idea. Basically I want to create a plexi-glass box containing controllable LEDs. I'm a total newbie but I've got the passion and patience to learn. I've read alot of guides, project tutorials etc. to have an idea and tried to figure out how to make mine work. But as a newbie I get easily confused. So please answer this: I want to use 9 LED strips (addressable WS2801 chipped). I want to have only 1 master strip that is controlled with arduino and other 8 slave strips will mimic its color&dim. I've seen some LED data repeater components online and thought they can do this job. Is this possible or am I being too optimistic? I know this is not pure arduino but considering what I want to achieve, this seemed like the place to ask it. Thank you.

One Arduino output should be able to control 9 strips, no 'repeater' needed. Just connect the Arduino pin to all nine strips.