A magic door.
The idea comes from Doraemon, a Japanese anime. This Random Door will have the ability to lead the user to anywhere they want.
The LCD will create a fake 3D space inside the open door, generating a virtual space. The space will respond to human interaction by tracking their faces. This will affect the perspective and movement of the inside world. There is also a accelerometer to make it respond to the movement by itself.
The simulated behavior of the 3D space will look familiar to this: