A maze is a path or collection of paths, typically from an entrance to a goal. The word is used to refer both to branching tour puzzles through which the solver must find a route, and to simpler non-branching ("unicursal") patterns that lead unambiguously through a convoluted layout to a goal. (The term "labyrinth" is generally synonymous with "maze", but can also connote specifically a unicursal pattern.) The pathways and walls in a maze are typically fixed, but puzzles in which the walls and paths can change during the game are also categorised as mazes or tour puzzles.
A small maze with one entrance and one exit
Mazes have been built with walls and rooms, with hedges, turf, corn stalks, straw bales, books, paving stones of contrasting colors or designs, and brick, or in fields of crops such as corn or, indeed, maize. Maize mazes can be very large; they are usually only kept for one growing season, so they can be different every year, and are promoted as seasonal tourist attractions. Indoors, mirror mazes are another form of maze, in which many of the apparent pathways are imaginary routes seen through multiple reflections in mirrors. Another type of maze consists of a set of rooms linked by doors (so a passageway is just another room in this definition). Players enter at one spot, and exit at another, or the idea may be to reach a certain spot in the maze. Mazes can also be printed or drawn on paper to be followed by a pencil or fingertip. Mazes can be built with snow.
Maze generation is the act of designing the layout of passages and walls within a maze. There are many different approaches to generating mazes, with various maze generation algorithms for building them, either by hand or automatically by computer.
There are two main mechanisms used to generate mazes. In "carving passages", one marks out the network of available routes. In building a maze by "adding walls", one lays out a set of obstructions within an open area. Most mazes drawn on paper are done by drawing the walls, with the spaces in between the markings composing the passages.
Maze solving is the act of finding a route through the maze from the start to finish. Some maze solving methods are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas others are designed to be used by a person or computer program that can see the whole maze at once.
The mathematicianLeonhard Euler was one of the first to analyze plane mazes mathematically, and in doing so made the first significant contributions to the branch of mathematics known as topology.
Mazes containing no loops are known as "standard", or "perfect" mazes, and are equivalent to a tree in graph theory. Thus many maze solving algorithms are closely related to graph theory. Intuitively, if one pulled and stretched out the paths in the maze in the proper way, the result could be made to resemble a tree.
A maze in which the paths are laid out like a railroad with switches and crossovers. Solvers are constrained to moving only forward. Often, a railroad maze will have a single track for entrance and exit.
These are like standard mazes except they use rules other than "don't cross the lines" to restrict motion.
Loops and traps maze
A maze that features one-way doors. The doors can lead to the correct path or create traps that divert you from the correct path and lead you to the starting point. The player may not return through a door through which he has entered, so dead ends may be created. The path is a series of loops interrupted by doors. Through the use of reciprocal doors[definition needed], the correct path can intersect the incorrect path on a single plane. A graphical variant of this maze type is an arrow maze.
Mazes in higher dimensions
It is possible for a maze to have three or more dimensions. A maze with bridges is three-dimensional, and some natural cave systems are three-dimensional mazes. The computer game Descent uses fully three-dimensional mazes. Any maze can be mapped into a higher dimension without changing its topology.
A maze in which numbers are used to determine jumps that form a pathway, allowing the maze to criss-cross itself many times.
A pattern like a long rope folded up, without any junctions or crossings.
Standard maze: Find a path from and back to the star.
Circular maze type: Find a route to the centre of the maze.
Loops and traps maze: Follow the arrows from and back to the star
Block maze: Fill in four blocks to make a road connecting the stars. No diagonals.
Number maze: Begin and end at the star. Using the number in your space, jump that number of blocks in a straight line to a new space. No diagonals.
Publications about mazes
Numerous mazes of different kinds have been drawn, painted, published in books and periodicals, used in advertising, in software, and sold as art. In the 1970s there occurred a publishing "maze craze" in which numerous books, and some magazines, were commercially available in nationwide outlets and devoted exclusively to mazes of a complexity that was able to challenge adults as well as children (for whom simple maze puzzles have long been provided both before, during, and since the 1970s "craze").
Some of the best-selling books in the 1970s and early 1980s included those produced by Vladimir Koziakin, Rick and Glory Brightfield, Dave Phillips, Larry Evans, and Greg Bright. Koziakin's works were predominantly of the standard two-dimensional "trace a line between the walls" variety. The works of the Brightfields had a similar two-dimensional form but used a variety of graphics-oriented "path obscuring" techniques. Although the routing was comparable to or simpler than Koziakin's mazes, the Brightfields' mazes did not allow the various pathway options to be discerned easily by the roving eye as it glanced about.
Greg Bright's works went beyond the standard published forms of the time by including "weave" mazes in which illustrated pathways can cross over and under each other. Bright's works also offered examples of extremely complex patterns of routing and optical illusions for the solver to work through. What Bright termed "mutually accessible centers" (The Great Maze Book, 1973) also called "braid" mazes, allowed a proliferation of paths flowing in spiral patterns from a central nexus and, rather than relying on "dead ends" to hinder progress, instead relied on an overabundance of pathway choices. Rather than have a single solution to the maze, Bright's routing often offered multiple equally valid routes from start to finish, with no loss of complexity or diminishment of solver difficulties because the result was that it became difficult for a solver to definitively "rule out" a particular pathway as unproductive. Some of Bright's innovative mazes had no "dead ends", although some clearly had looping sections (or "islands") that would cause careless explorers to keep looping back again and again to pathways they had already travelled.
The books of Larry Evans focused on 3-D structures, often with realistic perspective and architectural themes, and Bernard Myers (Supermazes No. 1) produced similar illustrations. Both Greg Bright (The Hole Maze Book) and Dave Phillips (The World's Most Difficult Maze) published maze books in which the sides of pages could be crossed over and in which holes could allow the pathways to cross from one page to another, and one side of a page to the other, thus enhancing the 3-D routing capacity of 2-D printed illustrations.
Adrian Fisher is both the most prolific contemporary author on mazes, and also one of the leading maze designers. His book The Amazing Book of Mazes (2006) contains examples and photographs of numerous methods of maze construction, several of which have been pioneered by Fisher; The Art of the Maze (Weidenfeld & Nicolson, 1990) contains a substantial history of the subject, whilst Mazes and Labyrinths (Shire Publications, 2004) is a useful introduction to the subject.
A recent book by Galen Wadzinski (The Ultimate Maze Book) offers formalized rules for more recent innovations that involve single-directional pathways, 3-D simulating illustrations, "key" and "ordered stop" mazes in which items must be collected or visited in particular orders to add to the difficulties of routing (such restrictions on pathway traveling and re-use are important in a printed book in which the limited amount of space on a printed page would otherwise place clear limits on the number of choices and pathways that can be contained within a single maze). Although these innovations are not all entirely new with Wadzinski, the book marks a significant advancement in published maze puzzles, offering expansions on the traditional puzzles that seem to have been fully informed by various video game innovations and designs, and adds new levels of challenge and complexity in both the design and the goals offered to the puzzle-solver in a printed format.
In 2012, the Kraay Family Farm in Alberta, Canada created the world's largest QR code in the form of a massive corn maze, popularly known as The Edmonton Corn Maze.
The Stanley Hotel in Estes Park, Colorado, which inspired Stephen King's novel The Shining (1977) but did not sport a hedge maze (despite one's being famously depicted in the 1980 film adaption), in November 2014 publicized an international design competition requesting entrants to propose designs to plant a 10,100-square-foot hedge maze, using 1,600 to 2,000 Alpine Currant hedge bushes, on the hotel's front lawn. On 31 January, the judges selected Jesse Alfaro's Evans, Colorado construction company.
Chartwell Castle in Johannesburg claims to have the biggest known uninterrupted hedgerow maze in the Southern world, with over 900 conifers. It covers about 6000 sq.m. (approximately 1.5 acres), which is around 5 times bigger than The Hampton Court Maze. The center is about 12m × 12m. The maze was designed and laid out by Conrad Penny.
Labirinto Verde,Nova Petrópolis, (Circular hedge maze built in 1989; Latitude 29°22'32.71"S Longitude 51°06'43.68"W)
Mazes in popular culture
Mazes on Television
Both Nubeluz and American Gladiators, from Peru and the United States respectively, featured a giant life-size maze used in competition. The object on both programs was for the contestants to find their way from the entrance to the exit as quickly as possible. On Nubeluz, the contestants took turns running through the maze and had a maximum of 1 minute to reach the exit; on American Gladiators, both contestants ran through the maze simultaneously and were given 45 seconds to find the correct solution. The giant maze was part of the game rotation on both programs concurrently, and was also retired from both programs simultaneously.