At every circular spot, there is a turnstile. Each door can be in one of two possible states, both with three doors with angles of 120 degrees between them. Put them in such a way that you can walk past each (without them needing to rotate) to get to any other hallway (the white part of the puzzle).
Puzzles in this genre
Every door can be in two states, let's call the state which has a door to the left of the center the "left state" and the other one the "right state".
The door in the bottom spot cannot be in the right state, because then the lower-right part of the puzzle would be disconnected with the rest. So it must be in the left state. Now the top-left spot cannot have a puzzle in the left state, since that would disconnect a circle between the two doors on the left. We can similarly argue that the spot on the right must contain a door in the left state.