Accoding to a BBC story:
The world's first moving building, an 80-storey tower with revolving floors giving a shifting shape, will be built in Dubai, its architect says. The Dynamic Tower design is made up of 80 pre-fabricated apartments which will spin independently of one another.
I am immediately horrified by this idea, but perhaps that is because I saw this really weird movie called Cube. 7 strangers wake up in an “endless kafkaesque maze containing deadly traps” (excellent imdb plot summary.) They are in a cube made up of dozens of smaller cubes, and at random intervals the cubes shift around. They have to find their way out, like solving Rubik’s cube from the inside as it tries to kill you. In case you were wondering Cube 2 was awful, not nearly as entertaining as the first.