maze

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A maze is a complex tour puzzle in the form of a complex branching passage through which the solver must find a route. In everyday speech, both maze and labyrinth denote a complex and confusing series of pathways, but technically the maze is distinguished from the labyrinth. The labyrinth has a single through-route with twists and turns but without branches; it is not designed to be as difficult to navigate as a maze is ^[1]. The pathways and walls in a maze or labyrinth are fixed (pre-determined). Maze-type puzzles where the given walls and paths may change during the game are covered under the main puzzle category of tour puzzles. The Cretan maze is the oldest.^[2]

Maze construction

Mazes have been built with walls and rooms, with hedges, turf, corn stalks, hay bales, books or with paving stones of contrasting colors or designs, 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, where 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.

A small maze.

Classical labyrinth.

A computer-generated maze.

Generating mazes

Maze generation is the act of designing the layout of passages and walls within a maze. There are many different approaches to generating mazes, where various maze generation algorithms exist for building them, either by hand or automatically by computer.

There are two main mechanisms used to generate mazes. "Carving passages" is where one marks out the network of available routes. "Adding walls" is where one lays out a set of obstructions within an open area. Most mazes drawn on paper are where one draws the walls, where the spaces in between the markings compose the passages.

Solving mazes

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 ^[3].

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

• the Barnes maze
• the Morris water maze
• the radial arm maze.

Mazes in computer games

This section does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (September 2009)

Mazes have long been a staple element in video games (e.g. the 80's classic Maziacs). In some games the entire objective of the game is to navigate mazes, while in other games the mazes are incorporated as only one element of the gameplay. A famous maze prank on the internet called, "The Excorsist Scary Maze Game", is a game where the player has to complete a maze. Upon completion of the game, the possessed face of Linda Blair from The Exorcist, pops up, along with two frighting screams. This game was created by Jeremy Winterrowd.

Other types of mazes

A plan of a Loops and Traps maze, Ridgewood, NJ

Logic mazes

See Logic maze. These are like standard mazes except they use rules other than "don't cross the lines" to restrict motion.

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 utilized fully three dimensional mazes. Any maze can be topologically mapped onto a three-dimensional maze^{[citation needed]}.

Picture maze

See Picture maze. A maze that forms a picture when solved.

Dead end maze

A maze game where the route creates the dead ends.

Turf mazes and Mizmazes

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

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. You may not return through a door which you have entered. The path is a series of loops interrupted by doors. The maze is not created with dead ends, but dead ends are created by doors that only open from the other side. The Halloween Maze in Ridgewood NJ is an example of this type of maze. Through the use of reciprocal doors, the correct path can intersect the incorrect path on a single plane.

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^[4], 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 Brightfield's mazes did not allow the various pathway options to be discerned so 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 Meyers (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^{[citation needed]}. 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 amount 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

Africa

• Serendipity Maze, Mouille Point, Cape Town, South Africa. Hedge maze by the sea.
• Soekershof Walkabout Mazes and Botanical Gardens, Robertson, Western Cape, South Africa. 13870 m² net area

Asia

India

• Adham Khan's Tomb, Delhi, India
• Bara Imambara, Lucknow, India

Dubai

• Gardens Shopping Mall, Dubai (World's Largest Indoor Maze ^[5])

Japan

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

Oceania

Australia

• The Maze, Perth, Western Australia
• Ashcombe Maze, Shoreham, Victoria, Australia.
• Mintaro Maze, Mintaro, South Australia

New Zealand

• The Great Maze, The Puzzling World, Wanaka, South Island (1.5 km of passages)

Europe

UK

• Noah's Ark Zoo Farm, Bristol, England (longest hedge maze in the world, planted 2003)
• Alnwick Castle Water Gardens Bamboo Maze, Northumberland. Designed by Adrian Fisher
• Blackpool Pleasure Beach Hedge Maze, Lancashire, England. Designed by Adrian Fisher
• Blake House Craft Centre, Braintree, Essex, England (Open July-Sept) [1]
• Blenheim Palace Hedge Maze, Oxfordshire, England. Designed by Minotaur Designs, Adrian Fisher, Randoll Coate and Graham Burgess., 1991
• St. Catherine's Hill, Hampshire near Winchester, old "Miz-Maze" or "Mizmaze" (unusual square design; path is a narrow groove)
• Castlewellan, Northern Ireland, world's largest permanent hedge maze [2]
• Chatsworth House, England (hedge maze)
• The Crystal Palace, England. A hedge maze built into a copse
• Greys Court 'Archbishop's Maze', Oxfordshire, England. Designed by Adrian Fisher, 1981
• Hampton Court Palace, England (hedge maze)
• Hoo Hill Maze, Shefford, Bedfordshire, England [3]
• Kentwell Hall, Long Melford, Suffolk, England. Designed Minotaur designs, Adrian Fisher, Randoll Coate and Graham Burgess.
• Leeds Castle, Maidstone, Kent, England. Designed by Minotaur Designs Randoll Caote , Adrian Fisher and Graham Burgess.
• Longleat, Wiltshire, England: hedge maze, designed by Greg Bright, 1978, and mirror maze, designed by Adrian Fisher; Labyrinth of Love, Renaissance style Rose garden labyrinth designed by Graham Burgess. Sun and Moon Maze designed by Randoll Coate.*
• Murray Star Maze, Scone Palace, Perth, Scotland (hedge maze). Designed by Adrian Fisher
• [4]
• Oak Lane Labyrinth, nr Bury St. Edmunds, Suffolk. Open all year round. Free entry.
• Paulton's Park, Hampshire, England (hedge maze)
• Richings Park Amazing Maize Maze, Richings Park, near Heathrow, England (Open July-Sept) [5]
• Saffron Walden, Essex, England (hedge maze) (The town also has an historic turf maze)
• Symonds Yat, Herefordshire, England
• Worden Park, Leyland, Lancashire, England

Greece

• Palace of Knossos
  

  

  Public hedge maze in the "English Garden" at Schönbusch Park, Aschaffenburg, Germany

Austria

• Schönbrunn Palace, Austria (small entrance fee, tower at the center to overlook the hedge maze)

Germany

• Altjeßnitz, Germany, Sachsen-Anhalt, near Dessau (hedge maze, c.1750) (51°41′35.7″N 12°19′23.9″E / 51.69325°N 12.323306°E / 51.69325; 12.323306 (Altjeßnitz maze))
• Aschaffenburg (Park Schönbusch), Germany, Bavaria (hedge maze, c.1829)
• Berlin (Erholungspark Marzahn), Germany (hedge maze)
• Erlebniswelt Hortus Vitalis - Der Irrgarten, Bad Salzuflen, Germany, North-Rhine-Westphalia (hedge maze)

Italy

• Villa Pisani, Stra, near Venice
• Porsenna's Maze, Chiusi, Tuscany (see Pliny's Italian labyrinth)

Inside the labyrinth of villa Pisani

Portugal

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

Spain

• Amaze'n Laberintos, Spain, Majorca, Alcudia, Playa de Muro (wooden maze, 1998)
• Parc del Laberint d'Horta, Barcelona, Spain (hedge maze)
• Labyrinth in the Way of Santiago - Spain Laberinto del Camino de Santiago - España.

Scandinavia

• The Labyrinth in Moomin World, Finland
• Labyrinthia, Silkeborg, Denmark
• Samsø, Denmark [6]

North America

• Magowan's Infinite Mirror Maze, Pier 39, San Francisco, California

Public maze at Wild Adventures theme park, Valdosta, Georgia

Maze at St. Louis Botanical Gardens

• Amazing Chicago's Funhouse Maze, Navy Pier, Chicago, Illinois, USA. Designed by Jack Rouse Associates and Adrian Fisher
• America's Largest Corn Maze, Shakopee, Minnesota, USA Sever's Corn Maze
• Children's maze (made out of packs of hay), Ashland Berry Farm, Ashland, Virginia, USA.
• Davis' Mega Maze, Sterling, Massachusetts USA (3-D adventure corn maze). Designed by Adrian Fisher [7]
• Dole Plantation, Wahiawa, Hawaii, (21°31′29.5″N 158°2′14.9″W / 21.524861°N 158.037472°W / 21.524861; -158.037472 (Dole Plantation)) home to the World's Largest Maze. [8]
• Labyrinthe du Hangar 16, Montreal, Canada. [9]
• Magnolia Plantation and Gardens (Charleston, South Carolina), USA
• Maize Quest Fun Park is the "Largest Collection of People-Sized Mazes in the World" with mazes made of fence, rope, stone, turf, corn, Invisible Dog Fencing, Straw Bales, Tiles, Living Bamboo, and Earthen Mounds. New Park, Pennsylvania, USA
• Mall of Georgia Paving Mazes, Atlanta, Georgia, USA. Designed by Adrian Fisher
• Maze Mania, Garden City, South Carolina USA (Interchangeable fence Maze appropriate for children and adults)
• Mohonk Mountain House hedge maze, New Paltz, New York
• Mystery Maze^[6], Wild Adventures theme park, Valdosta, Georgia - manufactured by Amazin' Mazes
• Noah's Ark Water Park Mirror Maze, Wisconsin Dells, USA. Designed by Adrian Fisher
• Norton Museum of Art West Palm Beach, USA. Pavement Maze, Serpent Mound and Turf Labyrinth. Designed by Adrian Fisher.
• Ridgewood Halloween Maze, Ridgewood, New Jersey, USA (Month of October, Loops and Traps Halloween-themed maze. Designed by Tyler Stewart.) Free attraction.
• Saunders Farm, Ottawa, Ontario, Canada. The largest collection of full-sized hedge mazes and labyrinths in North America (11).
• Skyline Caverns Mirror Maze, Front Royal, Virginia, USA. Designed by Adrian Fisher.
• The Maze at the Governor's Palace, Colonial Williamsburg, Virginia, USA
• The Maze on Centre Island, Toronto, Ontario, was a centennial gift to the city by its Dutch-Canadian community in 1967 (Topiary maze, open to public, free, year-round)
• Trail of Terror, Minneapolis, Minnesota, USA (annual event, 3/4 mile indoor Halloween-themed maze) ^[7]

Further reading

• H. Abelson and A. diSessa, Turtle Geometry: The Computer as a Medium for Exploring Mathematics, MIT Press (1980)
• Adrian Fisher, The Amazing Book of Mazes, Thames & Hudson, London / Harry N Abrams Inc, New York (2006) ISBN 978-0500512470
• Adrian Fisher, Armchair Puzzlers: Mad Mazes, University Books, San Francisco, USA (2005) ISBN 978-1575289786
• Adrian Fisher, Mazes and Follies, Jarrold Publishing, UK (2004) ISBN 978-1841651422
• Adrian Fisher, Mazes and Labyrinths, Shire Publications, UK (2003) ISBN 978-0747805618
• Adrian Fisher and Howard Loxton, Secrets of the Maze, Thames & Hudson, London (1997) / Barron’s Educational Series Inc, New York (1998) ISBN 978-0500018118
• Adrian Fisher and Jeff Saward, The British Maze Guide, Minotaur Designs, St Albans, UK (1991) - the definitive guide to British Mazes
• Adrian Fisher and Georg Gerster, The Art of the Maze, Weidenfeld & Nicolson, London (1990) ISBN 0-297-83027-9
• Adrian Fisher and Georg Gerster, Labyrinth - Solving the Riddle of the Maze, Harmony Books USA, New York (1990) ISBN 978-0517580998
• W.H. Matthews, Mazes and Labyrinths: Their History and Development (1927). Includes Bibliography. Dover Publications (1970) ISBN 0-486-22614-X
• Jeff Saward, Magical Paths, Mitchell Beazley (2002) ISBN 1-84000-573-4

See also

References

External links

Wikimedia Commons has media related to: Labyrinths

Look up maze in Wiktionary, the free dictionary.

Wikisource has the text of the 1911 Encyclopædia Britannica article maze.

• Maze Blog Learn how to draw and solve mazes. Stay current with a maze blog. Download printable mazes.
• Mazes on Silent animation's site (eng.)
• Briefing Room CNN's Barry Neild offers escape routes
• cornmazedir.com Directory of hundreds of mazes in the USA and Canada
• Images Mazes Real mazes that look like an inkblot portrait
• Labyrinth Society
• Labyrinthos Jeff Saward's website
• Learn how to draw mazes
• W.H. Matthews, Mazes and Labyrinths (1922) online version of W.H. Matthew's classic book
• Maze Algorithms This site explains the different types of mazes and how to generate and solve them
• Multiplayer Maze Game Flash-based free maze game in 2D
• 4D Maze Game John McIntosh's Java-based free maze game in 3D and 4D first-perspective
• Times Online: Britain's best mazes
• Ink Blot Mazes Maze Artist, Yonatan Frimer's page of image mazes that mix art and mazes.
• Labyrinth Online
• Quoridor.net Board and online game where players build maze