Realtime maze rebuilding

I saw movie The Maze Runner and I liked idea that maze is moving his walls by changing whole path. If someone doesn't know about The Maze Runner maze, it sounds like: "Every night, the Walls of the Maze change, repeating the same pattern every month." Currently I working on project and trying to achieve this. I already done maze generation at start, but I have no idea, how I should move maze walls to change whole maze.
Maybe there's smart people who can help me with that. I hope this is possible at all.
So anyone who has any idea how I can achieve that, please share it with me ;)

And sorry for broken english.