Dream Mechanics

Since the dream that I had the other night about randomly shifting floors, I've been trying to figure out how one would use rotating gears to create a random path.  In the dream, there were interlocking circular path disks, six set around a central seventh one in a larger disk, repeated again.

Thinking about what it would look like, I'm thinking there could be a straight path across the center of a disk, or a disk with a path that makes a sixty-degree turn, or a disk with a one-twenty-degree turn, or a  forked path, or a disk with two paths.  And their mirror images.  I'm thinkining there should be about twelve variations, depending on how complicated I want to be with the disk designs.  

To be truly random, each tile has an equal chance of turning left, right, or staying still.  If the circular track had a binary counter in it that counts 00 01 10, then the tiles could have one, too... but that wouldn't be random.  

I'm seeing a disk-rotation mechanism with toothless gears, but then I realize it would move cyclically.

I'm thinking I need to study how slot machines work.