Mazes are either branching puzzles or single-path unicursal routes
A maze is a path, or a web of paths, usually leading from an entrance to a goal. The word covers branching puzzles where you must choose your route and also unicursal designs that wind without any junctions to the centre; labyrinth often means the same thing, sometimes specifically the unicursal kind.
Builders have used almost anything. Hedges, turf, walls, rooms, tiles, paving and brick make lasting mazes, while corn stalks, straw bales, books and snow make temporary ones. Maize mazes can be huge and are usually replanted each growing season with a new layout, sold as seasonal tourist draws. Indoors, mirror mazes multiply reflections into corridors that do not exist, and some mazes are simply rooms linked by doors. Others live on paper, traced with a pencil or a finger, and some puzzles even let the walls shift during play.
Designers generate layouts either by carving passages, marking out the network of open routes, or by adding walls, scattering obstacles across an open area, whether working by hand or letting a computer algorithm do it. Solving methods split too: some suit a walker inside with no map, others a person or program that can see the whole plan at once.
Leonhard Euler was among the first to analyse flat mazes mathematically, work that made early significant contributions to topology. A maze with no loops is called standard or perfect and is equivalent to a tree in graph theory, which is why so many solving algorithms borrow from that field. Psychologists run rats and mice through mazes to study spatial learning. Variants include dexterity puzzles that roll a ball along a track, recursive mazes that repeat inside holes at ever smaller scales, one-way door mazes that trap walkers in loops, and picture mazes whose solution draws an image.
Denmark's Samsø Labyrinten, at 60,000 square metres, claims to be the world's largest permanent maze, and a Dubai mall hosts the largest indoor one. Northern Ireland's Carnfunnock hedge maze, shaped like the province, won a 1985 design competition.
Source: Maze
