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Perhaps this place is possessed by a demon or inhabited by a spirit, making it a Genius Loci, or it was built with tracks, pistons and engines to move according to the beat of an arcane clockwork heart (or high-tech AI), but usually, there is no way to stop or even detect the mechanism. You must let it herd you or puzzle it out the trick it wants. Alien Geometries (especially Oh Look, More Rooms!) may complicate it still further, along with any door being possibly a Cool Gate. As can the possibility of being eaten.

Sometimes it is, in fact, a mind game: the character's sense of direction is confused, or he can no longer recognize which parts he has been through.

The Maze is the parent trope. If paired with an Psychological Torment Zone, it becomes a deadly Closed Circle.

Examples

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Anime & Manga

In The Cat Returns, the king of cats tries to trap Haru-chan by having her traverse a maze, and sending in cats holding fake walls to block the path. Unusually, the Baron is able to knock them unconscious and clear their path.
- The original manga gave us a labyrinth built on sliding concentric circles. Hilariously, this produces, at certain brief intervals, completely clear paths towards the center.
The Maze card can do this in Card Captor Sakura, also creating Escher-like Alien Geometries.
In the episode of Ulysses 31 featuring Theseus and the Minotaur, at one point the whole Labyrinth starts to move around, threatening to separate or even crush the heroes.
Played to hilarious effect in the General White arc of Dragon Ball. Goku and Android 8 ("Ha-chan") must get through a maze to reach the Red Ribbon officer. The maze is completely normal, except for a single wall which can be toggled to block one of the two passages out. After running back and forth between the apparent dead-ends for a while, Goku and Android 8 finally decide to just split up and take both passages at once. Top-notch security system there, General.
In Bleach, Szayel Aporro Granz can control the passages of his lair with his mind. Any path someone tries to take will lead back to him.

Board Games

The board game The aMAZEing Labyrinth has this as its gameplay mechanic, as each player can choose to either move their own piece or push a new tile onto the board, displacing a row or column.
The flowchart — I mean dungeon — in Drakon is built a little at a time and changes frequently.
The classic Wizwar has entire sections of its labyrinth spin in place.

Comics

Doctor Strange's Sanctum Sanctorum is a (relatively) benign example. Strange's friends and allies have no trouble getting around, but it becomes a dangerous trap for his enemies.

Films

The Labyrinth in Labyrinth.
The Virtual Room in Spy Kids.
The temple in Alien vs. Predator. It's designed as a challenging hunting ground for young Predators.
The Thir13en Ghosts glass house.
Highly malicious non-sentient (we hope) one in Cube and its sequels.
The labyrinth in Pan's Labyrinth actually helps Ophelia at one point, opening a direct path for her before closing back up to keep Vidal away a little longer.
The eponymous Dark City.
The Definitely Final Dungeons in Hellboy I and II (Rasputin's tomb and the Elf Kingdom, respectively).
The world of the Cenobites in Hellbound Hellraiser II is presented as an infinite, every changing dark labyrinth of stone under the control of a floating rotating silver lozenge called Leviathan.
A less extreme example is the rotating Grand Staircase in Harry Potter's Hogwarts Castle. Although not truly a maze, it's still easy for students to get lost on their way to class.
The Hedge Maze in The Shining. It only appears in Kubrick's version, not the book or the TV miniseries (which feature a topiary instead).

Literature

Warhammer 40000 novels seem to use this trope a lot. Examples include:
- In Dan Abnett's Gaunt's Ghosts novel First & Only, Mkoll is certain that their map does not match their path through an ancient structure, and that their path had changed from five minutes ago. (His coming from Tanith, where the trees can move, gives him acute sensitivity to such changes.)
- In Dan Abnett's Brothers of the Snake, the Royal Mound appears to be this, although that may be psychic effects.
- In Dan Abnett's Horus Heresy novel Legion (are we sensing a theme here?), Grammaticus, in the city of Mon Lo, finds himself unable to orient himself. At one point he concludes he just went one street too far, and doubles back, and what he expected was not there. (He can determine that there are strong psychic influences, but not stop his bewilderment.)
- In Graham McNeill's Ultramarines novel Dead Sky Black Sun, the city in the Eye of Chaos (possibly with some Alien Geometries help).
  There was no rhyme or reason to the layout of the fortress, if even such a thing truly existed. Travelling down the same street was no guarantee of arriving at the same place, and doubling back did not return to them to whence they had begun.
House of Leaves combines this with Darkness Equals Death.
The Shrub Maze in Harry Potter did this (with tons of traps and hazards).
- Not to mention the film version, in which the maze is truly alive.
- So did Hogwart's Castle.
The Logrus in The Chronicles of Amber: it is an ever-changing labyrinth where you had to rely on your luck and intuition to ever find a way out.
The Maze on Minos in Terry Pratchett's The Dark Side Of The Sun. It doesn't shift once formed, but everyone who goes in experiences a different maze pattern.
A slightly more primitive version appears in The Book of D'Ni. A "maze game" exists which is composed of rooms that shift around. It's powered by slave labor, and fatalities are the norm when they turn the rooms.
In the Castle Perilous series, the entire castle acts this way. The outer regions are especially chaotic and unstable, the Guest areas are relatively safe with only a few minor gravity and perspective shifts every so often. Since the castle is also a massive Portal Network to 144,000 worlds, a trip to the bathroom can lead to adventure, terror, or the bathroom.
In Edgar Rice Burroughs's The Gods of Mars, John Carter and Tars Tarkus are trapped in such a maze — with monsters for more fun.
One of the protections on the Blue Temple treasury in Fred Saberhagen's Second Book of Swords.
Both the Forest of Wayreth and the Hedge Maze surrounding the Silver Stair in the Dragonlance series qualify.
The maze in M.R. James's "Mr. Humphreys' Inheritance".
The Labyrinth in Death Gate. It was supposed to be relatively benevolent, keeping the Patryns trapped while they were 'reformed', but when those charged with controlling it died, it mutated and became a labyrinth of death instead...
David Eddings novel The Sapphire Rose includes a maze which changes so no one can ever leave. The heroes defeat it by smashing a hole in the ceiling and climbing onto the top, saying "if you don't like the game, don't play it."
The Labyrinth built by Daedalus (yes, that Daedalus) in Percy Jackson and the Olympians is said to grow and change over time. It is now under the entire United States, and possibly the entire world. It's tied to Daedalus's life force, so if he dies, it will collapse.
Felka, of the Revelation Space series, created a miniature version to run mice through. She was studying emergent behavior and wondered if it was possible to produce a mechanical AI in this manner. Note: Felka is effectively insane.
The eponymous forest of the Enchanted Forest Chronicles by Patricia C. Wrede is a variant of this - its geography is constantly shifting, such that the royal castle can at best be said to be located somewhere near the center of the kingdom. This is because it explicitly obeys fairytale/mythical/plot-determined geography, on top of showing signs of low-level sentience. Directions must be given in classic fairytale style and obeyed precisely if a traveler wants to reach their destination. Even then, the forest can effectively trap or re-route someone who it doesn't want to reach their destination, or make a journey quicker for someone it wants to aid. So heroes can always be sure to arrive just in the nick of time.
In The Maze Runner, all the main characters are trapped in a small, protected area called the Glade, which is inside a giant maze that rearranges itself every night.
The Boy Who Reversed Himself had a 4 dimensional version of this, used by the 4-space creatures to try and convince the main characters to show them how to get to 3-space (our plane of existence).
Pixel is confined to one in the sixth book of the Diadem series. Not only does the maze shift around silently, there's some sort of giant rat monster after him. He escapes by predicting the walls' next move and jamming them open.
Keys to the Kingdom has the Great Maze, the section of the House used to train the Glorious Army of the Architect. It is a one thousand by one thousand grid of one mile by one mile tiles which randomly switch their positions every day.
In one of the many Flashbacks of BIONICLE Legends #4: Legacy of Evil, the six Piraka try to murder their boss the Shadowed One, but find that his transforming fortress has been leading them into his trap.
In The Wheel of Time, the realm of the Snakes and Foxes is one giant mobile maze that bends to their very whims. Brigitte tells Mat that she wandered around in there with Gaidal Cain for weeks without crossing the same room twice. Fortunately, Mat gets out because he's Born Lucky.

Live Action TV

In the Doctor Who episode "The Horns of Nimon", the alien Nimon demand sacrifices from the Skonnon Empire to provide for them. They use victims from the planet Aneth, who find that the walls seal behind them. (A Twice Told Tale based on the legend of Theseus and the Labyrinth.) It turns out the labyrinth is actually a giant computer and the changing walls are the circuits making connection. The entrance is actually a hologram of a wall.
Also used in the newer episode, "The God Complex", where the Doctor, Rory and Amy are trapped in what appears to be a seventies hotel, with corridors that twist and shift and can end up going on for miles. The above-mentioned Nimon also receives a Shout Out- the Monster of the Week is said to be a distant evolutionary cousin of it.
In an episode of The Avengers, "The House That Jack Built", Mrs. Emma Peel gets trapped inside one of these created by a long time colleague.
In the One Episode Wonder Lost In Oz, Loriellidere's labyrinth is easy to get into, but when the heroes try to escape, the hallways shift and lead them straight back to the Witch.
In the Buffy the Vampire Slayer episode Fear Itself, the Alpha Delta fraternity�s haunted house turns into one of these.
This
This was one of the games on the automotive game show Full Metal Challenge.
In Star Trek: Voyager, a Negative Space Wedgie turned the whole ship into one of these.

Tabletop RP Gs

Dungeons & Dragons gives us "Neth, the Plane that Lives", a sentient dimension which resembles a Womb World, complete with breathable pink fluid in its passages - and a habit of sealing randomly-selected visitors into bubbles filled with digestive fluid. It later spawns a copy of their head from the wall of its "brain" and talks with their voice along with dozens of previous victims'.
- The maze created by the Maze spell to momentarily trap a character is also described as shifting.
The realm of Tzeench in Warhammer / 40k is like this. It is described as appearing to mortals as a huge crystalline labyrinth that endlessly shifts and changes to trap any would-be intruders. At its center sits the Impossible Fortress, a huge structure not bound by the laws of physics, geometry or sanity. Windows and doors constantly appear and disappear on its surface, and interior rooms and passages keep constantly changing. Even gravity changes in strength and direction at random.
The Hedge is a realm that lies between Arcadia and the "real world" in Changeling The Lost, forming an ever-shifting hedge maze that keeps the captives of the True Fae from easily escaping back to Earth. It can be reached via portals that temporarily borrow real-world doorframes. The Hedge's thorns are capable of tearing away small pieces of a traveller's soul as they pass through, and terrible ravenous creatures called Briar Wolves dwell there, but it's still generally better to risk it than stay in Arcadia.

Video Games

Kingdom Of Loathing has a hedge maze which you must rotate using puzzles of said hedge maze.
the white chamber
Descent II had some areas like this, particularly in the later levels, which often featured doors that locked behind you, or fences and forcefields that would literally appear out of nowhere, boxing you in. Sometimes you had to counteract the effect by destroying a control panel, and sometimes you had to find a way around, usually involving a secret passage of some sort. While the main game was bad enough, the secret levels were this trope incarnate, and maddeningly difficult to find your way through, even becoming Un Winnable in certain circumstances (at which point you could usually exit the level, but you couldn't retry it). Did I mention that all of this game's mazes were 3D?
Final Fantasy XI has the Sacrarium, which possesses a maze that changes it's layout every game day.
Tartarus in Persona 3, The Abyss of Time in Persona 3 FES, and the TV World in Persona 4 are all labyrinths that generate randomly each time you enter, with the exception of a few key rooms. In addition, leaving a room in Persona 3 typically causes the stairway to vanish behind you.
Strange Journey has some very nasty examples, such as the sticky floors of Sector Delphinus or the endless illusions of Sector Grus.
Silent Hill 3: The Borley Haunted Mansion has a Mobile Hallway that you must negotiate while running from the Advancing Red Fog of Doom.
- Silent Hill 2 has a rotating room puzzle in the Labyrinth.
- In fact, the whole town of Silent Hill could be called this, particularly the Dark World.
Planescape: Torment has Rubikon, a dungeon simulator built in Limbo by a group of Modrons to determine what the deal is about dungeons and adventurers' relation to them. As Modrons are beings of pure law while Limbo is the plane of pure chaos, the place is insane. The dungeon can be reset to respawn items and baddies, and also set to three difficulty levels; doing so will change the layout. It also offers decent experience and some unique loot, as well as an additional party member.
Morte: It feels like I'm in a cuckoo clock. A cuckoo cuckoo clock.
- Ravel's Black-Barbed Maze from Planescape: Torment. She seems to have control over its changing shape.
- Sigil itself, in so many ways. Any given doorway or archway can become a portal somewhere else, under the right conditions. The Lady's servants, the Dabus, are constantly arranging and rearranging the structural layout of the city, according to whims that baffle life-long natives. And certain parts of the city can awaken to consciousness and, like living beings, grow and even give birth to new avenues.
The Cemetery level in Left 4 Dead 2's The Parish campaign is a more meta example. While the level is static after it's loaded, the path to the exit changes each time you play. This demonstrates the new power of the AI Director.
Borderline example is the castle in Castlevania. It's a "creature of chaos", so it changes layout between games.
Shifting mazes are a standard feature of MUDs. It's common to navigate them by dropping markers in the rooms, though it's still tough to make it through before it shifts again. And if there are mobs that pick up items left lying around, then...
Primal has a Mobile Maze that must be shifted by the player. Three switches must be found that change the configuration of the maze. Activating a switch makes it possible to reach the next switch. The final switch opens a straight path through the center of the maze.
The Aperture Science Computer Aided Enrichment Center in Portal can be considered a Mobile Maze in that the walls are constantly shifting in order to keep test subjects like Chell trapped inside the designated testing area. Exits can be opened or (more often) closed, not to mention that the entire place can, at any moment, be flooded with a deadly neural-toxin.
One of the earliest examples of this trope applied to video games is Pulsar, a 1980 arcade game by Sega. The player controls a tank driving around a maze, and every couple of seconds a random segment of the maze wall shifts positions, closing off one path while opening up another. A tank that is carelessly parked in the wrong place can even be crushed by a shifting wall, a most painful way to die.
Sky Keep is a perfect example of the player-controlled variation, with consoles that change the rooms like the tiles in a slider puzzle.

Web Comics

Girl Genius: Castle Heterodyne, as shown here.
"The door we came through — it never lead here before."
In A Modest Destiny, Fluffy the Vampire Lord has created one of these to make money. He reasons that evil overlords are constantly having to commission new dungeons for heroes to crawl around in, so he makes one that can restructure itself on demand, thus selling a nearly infinite variety of dungeons for only a little more than the price of one. Unfortunately, he then goes and get trapped in it when he goes in and the exit moves.
In American Barbarian, the god appears to do this to the temple.
In Our Little Adventure, the second labyrith has a sign warning of this.

Web Original

The Tale Of Gaven Morren: The City of Miir becomes this at the behest of The Shadows.

Western Animation

Code Lyoko: Carthage/Sector Five. Bonus points for not only being deadly in its own right (not true death, just devirtualization in most cases), but also having dangerous creatures inside it.
An episode of Batman The Animated Series introduced The Riddler with a "Riddle of the Minotaur" video game and a real-life amusement park labyrinth based on it, with robotic monsters and moving walls.
- The Mad Hatter had a similar trick.
The Illuminati's main prison in Gargoyles was based around one of these: a condemened hotel with constantly shifting booby-trapped rooms.
In one episode of Pinky And The Brain, the scientists experimenting on the mice put them into a virtual reality maze with rotating corridors.
The Cave of Two Lovers in Avatar The Last Airbender has shifting walls caused by the excavations of mischievous badgermoles.
Chong: The tunnels� they are a-changin�.
Played with in Ben 10 Ultimate Alien in that,instead of a maze, it's a Three-dimensional cube called the Perplexehedron (a security system for a Plot Coupon) full of many death traps, including guards. Bonus points for making the only way too the plot coupon involve setting off all the guards.

Real Life

Done at Halloween Horror Nights Orlando for the 2001 event with the haunted maze "Run", which was placed in a maze of fencing that would, on occasion, change its paths to confuse repeat visitors (often as simple as a scareactor closing a door). Unfortunately, it was stopped after about a week due to the inevitable back-ups and confusion resulting in visitors walking through the wrong door.

Key Under the Doormat

Building Tropes

Museum Of Boredom

Mixed Metaphor

Added Alliterative Appeal