Maze

Not to be confused with Maize.

For other uses, see Maze (disambiguation).

A hedge maze at Longleat stately home in England

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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, but also can 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.

Maze construction

A small maze with one entrance and one exit

Snow maze with one way, one entrance and one exit. Built within 10 minutes.

Mazes have been built with walls and rooms, with hedges, turf, corn stalks, hay 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.

Generating mazes

Main article: Maze generation algorithm

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.

Solving mazes

Main article: Maze solving algorithm

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 mathematician Leonhard 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.

Mazes in psychology experiments

Mazes are often used in psychology experiments to study spatial navigation and learning. Such experiments typically use rats or mice. Examples are:

• Barnes maze
• Morris water maze
  • Oasis maze
• Radial arm maze
• Elevated plus maze
• T-maze

Other types of mazes

Ball-in-a-maze puzzles

Dexterity puzzles which involve navigating a ball through a maze or labyrinth.

Block maze

A maze in which the player must complete or clear the maze pathway by positioning blocks. Blocks may slide into place or be added.

Hamilton maze

A maze in which the goal is to find the unique Hamiltonian cycle.

Linear or railroad maze

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.

Logic mazes

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, 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.

Number maze

A maze in which numbers are used to determine jumps that form a pathway, allowing the maze to criss-cross itself many times.

Picture maze

A standard maze that forms a picture when solved.

Turf mazes and mizmazes

A pattern like a long rope folded up, without any junctions or crossings.

Gallery

• 

  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 and Nicholson, 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.

Mazes open to the public

Asia

Dubai

• Gardens Shopping Mall, Dubai (world's largest indoor maze)

Japan

• Hikimi no Meiro, Kiso, Nagano, Japan
• Kyodai Meiro Palladium, Nikkō, Tochigi, Japan
• Sendai Hi-Land, Sendai, Miyagi, Japan
• Shirahama Energy Land, Shirahama, Wakayama, Japan

Pacific

New Zealand

• Amazing Maze n' Maize
• The Great Maze

Europe

Austria

• Schönbrunn Palace, Vienna, has a large hedge maze in its gardens.

Belgium

• Loppem Castle maze

Denmark

• Labyrinthia, Silkeborg
• Samsø Labyrinten (The world's largest permanent maze, 60.000 m²)

Germany

• Hortus Vitalis – Der Irrgarten, Bad Salzuflen (hedge maze)

Greece

• Labyrinth Park near Hersonissos, Crete (extends to approximately 1.300 m²)

Italy

• Castello di Masino, Caravino 10010, Torino, Italia
• Porsenna's Maze, Chiusi, Tuscany (see Pliny's Italian labyrinth)
• Villa Pisani, Stra, near Venice (45.409587°N 12.013131°E / 45.409587; 12.013131)
• The labyrinth of Franco Maria Ricci at Fontanellato (44.853989°N 10.146446°E / 44.853989; 10.146446)

Netherlands

• Waterlabyrinth, Nijmegen, designed by Klaus van de Locht, 1981 (51.85016°N 5.860471°E / 51.85016; 5.860471 (Labyrinth))
• Doolhof Ruurlo, Ruurlo, designed by Daniel Marot, based on the design for Hampton Court Maze (52.078266°N 6.433654°E / 52.078266; 6.433654 (Doolhof Ruurlo))

Portugal

• Parque do Arnado, Ponte de Lima, District of Viana do Castelo
• Parque de São Roque, District of Porto
• Forest Reserve of Pinhal da Paz, São Miguel Island, Azores

Spain

• Alcázar of Seville, Seville
• Corn Laberynth in the Camino de Santiago, León
• Parc del laberint d'Horta, Barcelona, (41.440235°N 2.145769°E / 41.440235; 2.145769 (Parc del laberint))
• Parc de la Torreblanca, Esplugues de Llobregat (41.37856°N 2.054628°E / 41.37856; 2.054628 (Labyrinth))
• Parque de El Capricho, Madrid
• Laberinto de Villapresente, Cantabria. With 5,625qm, it is the largest maze in Spain.
• Parque de Tentegorra, Murcia
• Royal Palace of La Granja de San Ildefonso, Segovia (40.5352°N 3.5956°W / 40.5352; -3.5956 (Labyrinth Royal Palace of La Granja de San Ildefonso))

UK

• Blake House Craft Centre, Braintree, Essex, England (Open July–September)
• Carnfunnock Country Park, Northern Ireland. A hedge maze in the shape of Northern Ireland and winner of 1985 Design a Maze competition.
• Castlewellan, Northern Ireland, world's largest permanent hedge maze
• Chatsworth House garden maze, planted with 1,209 yews.
• Cliveden House Originally laid out in 1894 and re-opened to the public in 2011, consisting of 1100 Yew trees
• Crystal Palace Park, South London. Laid out in the 1870s, this is the largest maze in London.
• Glendurgan Garden, Cornwall. A cherry laurel hedge maze created in 1833.
• Hampton Court Maze. A famous historic maze in the Palace gardens.
• Hever Castle Maze, Hever, Kent. Yew tree maze and a splashing water maze
• Hoo Hill Maze, Shefford, Bedfordshire, England
• Norwich Cathedral, Norfolk, England. A labyrinth in the Cloister Garth. Laid to commemorate the Golden Jubilee of HM Queen Elizabeth II in 2002.
• Richings Park Amazing Maize Maze, Richings Park, near Heathrow, England (Open July–September)
• Saltwell Park, Gateshead, Tyne and Wear, England. A yew-tree maze restored to its original condition in 2005 and open to the public during park opening hours.
• Somerleyton Hall, Suffolk, England. A yew hedge maze designed and planted in 1846 by William Nesfield.
• York Maze. Located near RAF Elvington and constructed using maize (Dalek corn) plants, the maze was created to celebrate the 50th anniversary of Doctor Who.

North America

Public maze at Wild Adventures theme park, Valdosta, Georgia, United States. It was removed before the 2010 season.

Maze at Missouri Botanical Garden in St. Louis

Canada

• 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.

USA

• 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.
• Dole Pineapple Plantation, Oahu.
• Tanglewood Music Center Hedge Maze, Lenox and Stockbridge, Massachusetts.

South Africa

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.

South America

Brazil

• 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

Fictional mazes

• The film adaptation of Stephen King's 1977 novel, The Shining (1980), includes a "harrowing" scene featuring Jack Torrance and Danny Torrance in an "ominous" hedge maze.

See also

• Celtic maze
• Corn maze
• Crop circle
• Hedge maze
• Labyrinth
• List of maze video games
• Logic Quest 3D
• Radial arm maze

Further reading

• Abelson, H. & diSessa, A. (1980). Turtle Geometry: The Computer as a Medium for Exploring Mathematics. MIT Press. CS1 maint: Uses authors parameter (link)
• Fisher, Adrian (2006). The Amazing Book of Mazes. London: Thames & Hudson and New York: Harry N Abrams Inc. ISBN 978-0-500-51247-0. 
• Fisher, Adrian & Gerster, Georg (1990). The Art of the Maze. London: Weidenfeld & Nicolson. ISBN 0-297-83027-9. CS1 maint: Uses authors parameter (link)
• Fisher, Adrian & Loxton, Howard (1997). Secrets of the Maze. London: Thames & Hudson. ISBN 978-0-500-01811-8. 
• Fisher, Adrian & Saward, Jeff (1991). The British Maze Guide. St Albans, UK: Minotaur Designs. CS1 maint: Uses authors parameter (link) The definitive guide to British Mazes.
• Martineau, John Southcliffe (2005). Mazes and Labyrinths: In Great Britain. Wooden Books. ISBN 978-1-904263-33-3. 
• Matthews, W. H. (1927). Mazes and Labyrinths: Their History and Development.  Includes "Bibliography". Mazes and Labyrinths. Dover Publications. 1970. ISBN 0-486-22614-X. 
• Saward, Jeff (2002). Magical Paths. Mitchell Beazley. ISBN 1-84000-573-4. 

External links

• "Britain's best mazes". Times Online. 21 August 2006. 
• Labyrinth Society official web page
• Neild, Barry (29 September 2006). "Shortcuts: Escaping a maze". CNN Briefing Room.