complex system of paths or tunnels in which it is easy to get lost (同)labyrinth
affect with wonder; "Your ability to speak six languages amazes me!" (同)astonish, astound
a frequently prescribed benzodiazepine (trade name Restoril); takes effect slowly and lasts long enough to help those people who wake up frequently during the night (同)Restoril
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.[1]) 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.
Contents
1Maze construction
2Generating mazes
3Solving mazes
4Mazes in psychology experiments
5Other types of mazes
5.1Gallery
6Publications about mazes
7Mazes open to the public
7.1Asia
7.1.1Dubai
7.1.2Japan
7.2Pacific
7.2.1New Zealand
7.3Europe
7.3.1Austria
7.3.2Belgium
7.3.3Denmark
7.3.4Germany
7.3.5Greece
7.3.6Italy
7.3.7Netherlands
7.3.8Portugal
7.3.9Spain
7.3.10UK
7.4North America
7.4.1Canada
7.4.2USA
7.5South Africa
7.6South America
7.6.1Brazil
8Mazes in popular culture
8.1Mazes on Television
8.2Fictional mazes
9See also
10References
11Further reading
12External links
Maze construction
A small maze with one entrance and one exit
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,[2] 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.[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:
Barnes maze
Morris water maze
Oasis maze
Radial arm maze
Elevated plus maze
T-maze
Other types of mazes
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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.[4][5]
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.
A plan of a Loops and Traps Maze, Ridgewood, NJ 2008
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.[citation needed]
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,[6] 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.[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 & 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.
Mazes open to the public
Asia
Dubai
Gardens Shopping Mall, Dubai (world's largest indoor maze)[7]
Japan
Hikimi no Meiro,[8] Kiso, Nagano, Japan
Kyodai Meiro Palladium,[9] Nikkō, Tochigi, Japan
Sendai Hi-Land,[10] Sendai, Miyagi, Japan
Shirahama Energy Land,[11] Shirahama, Wakayama, Japan
Pacific
New Zealand
Amazing Maze n' Maize
The Great Maze at Puzzling World
Europe
Austria
Schönbrunn Palace, Vienna, has a large hedge maze in its gardens.
Swarovski Crystal World, Wattens, Tyrol, has a hand-shaped hedge maze in its gardens.
Belgium
Loppem Castle maze
Denmark
Samsø Labyrinten (The world's largest permanent maze, 60.000 m2)[12][13]
Germany
Hortus Vitalis – Der Irrgarten,[14] Bad Salzuflen (hedge maze)
Greece
Labyrinth Park near Hersonissos, Crete (extends to approximately 1.300 m2)[15][16]
Italy
Castello di Masino, Caravino 10010, Torino, Italia
Porsenna's Maze [it],[17] Chiusi, Tuscany (see Pliny's Italian labyrinth)
Villa Pisani, Stra, near Venice (45°24′35″N12°00′47″E / 45.409587°N 12.013131°E / 45.409587; 12.013131 (Maze))
The labyrinth of Franco Maria Ricci at Fontanellato[18] (44°51′14″N10°08′47″E / 44.853989°N 10.146446°E / 44.853989; 10.146446 (Maze))
Netherlands
Waterlabyrinth, Nijmegen, designed by Klaus van de Locht, 1981[19] (51°51′01″N5°51′38″E / 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[20] (52°04′42″N6°26′01″E / 52.078266°N 6.433654°E / 52.078266; 6.433654 (Doolhof Ruurlo))
Portugal
Parque do Arnado,[21] Ponte de Lima, District of Viana do Castelo
Parque de São Roque,[22] District of Porto[23]
Forest Reserve of Pinhal da Paz,[24] São Miguel Island, Azores
Spain
Alcázar of Seville, Seville
Corn Laberynth in the Camino de Santiago, León [25]
Parc del laberint d'Horta, Barcelona,[26] (41°26′25″N2°08′45″E / 41.440235°N 2.145769°E / 41.440235; 2.145769 (Parc del laberint))
Parc de la Torreblanca, Esplugues de Llobregat (41°22′43″N2°03′17″E / 41.37856°N 2.054628°E / 41.37856; 2.054628 (Labyrinth))
Parque de El Capricho, Madrid
Laberinto de Villapresente,[27] Cantabria. With 5,625qm, it is the largest maze in Spain.
Parque de Tentegorra,[28] Murcia
Royal Palace of La Granja de San Ildefonso,[29] Segovia (40°32′07″N3°35′44″W / 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)[30][31]
Carnfunnock Country Park, Northern Ireland. A hedge maze in the shape of Northern Ireland and winner of 1985 Design a Maze competition.[32]
Castlewellan, Northern Ireland, world's largest permanent hedge maze[33][34]
Chatsworth House garden maze, planted with 1,209 yews.
Cliveden House Originally laid out in 1894, the maze was restored 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.[35]
Glendurgan Garden, Cornwall. A cherry laurel hedge maze created in 1833.[36]
Hampton Court Maze. A famous historic maze in the Palace gardens.[37]
Hever Castle Maze, Hever, Kent. Yew tree maze and a splashing water maze[38]
Hoo Hill Maze, Shefford, Bedfordshire, England[39][40]
Norwich Cathedral, Norfolk, England. A labyrinth in the Cloister Garth. Laid to commemorate the Golden Jubilee of HM Queen Elizabeth II in 2002.[41]
Richings Park Amazing Maize Maze, Richings Park, near Heathrow, England (Open July–September)[42]
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.[43]
Somerleyton Hall, Suffolk, England. A yew hedge maze designed and planted in 1846 by William Nesfield.[44]
York Maze. Located near RAF Elvington and constructed using maize (Dalek corn[45]) plants,[46] the maze was created to celebrate the 50th anniversary of Doctor Who.[45]
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.[47][48]
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.[49][50]
Dole Pineapple Plantation, Oahu.
Tanglewood Music Center Hedge Maze, Lenox and Stockbridge, Massachusetts.[51]
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.[52]
South America
Brazil
Labirinto Verde,[53] Nova Petrópolis, (Circular hedge maze built in 1989; Latitude 29°22'32.71"S Longitude 51°06'43.68"W)
Mazes in popular culture
This section needs expansion. You can help by adding to it. (February 2018)
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; on American Gladiators, both contestants ran through the maze simultaneously. The giant maze was part of the game rotation on both programs concurrently, and was also retired from both programs simultaneously.
Fictional mazes
The film adaptation of Stephen King's 1977 novel, The Shining (1980), includes a harrowing[49] scene featuring Jack Torrance and Danny Torrance in an ominous[50] hedge maze.
See also
Celtic maze
Corn maze
Crop circle
Hedge maze
Labyrinth
List of maze video games
Radial arm maze
References
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^Lappa Valley Steam Railway – Trevithick Brick Path Maze, Lappa Valley Steam Railway, archived from the original on 12 August 2009, retrieved 13 June 2010
^Maze to Tree Archived 12 April 2016 at the Wayback Machine. YouTube (2007-12-23). Retrieved on 2011-06-18.
^de Ruiter, Johan (2017). Hamilton Mazes - The Beginner's Guide.
^Friedman, Erich (2009). "Hamiltonian Mazes". Erich's Puzzle Palace. Archived from the original on 16 April 2016. Retrieved 27 May 2017.
^Mazes, Vladimir Koziakin (Grosset & Dunlap, 1971) ISBN 0-448-01836-5
^Retail Arabia to open French hypermarket Géant in The Gardens Shopping Mall | Nakheel Properties Archived 2 January 2009 at the Wayback Machine. AMEinfo.com. Retrieved on 2011-06-18.
^welcome to hikimi town!! Archived 13 July 2008 at the Wayback Machine. Iwami.or.jp. Retrieved on 2011-06-18.
^巨大迷路パラディアム Archived 17 December 2007 at the Wayback Machine. Kinugawa.ne.jp. Retrieved on 2011-06-18.
^仙台ハイランド ホームページ Archived 14 April 2008 at the Wayback Machine. Hi-land.co.jp. Retrieved on 2011-06-18.
^：：白浜エネルギーランド：： 移転連絡 Archived 7 May 2008 at the Wayback Machine. Royalpines.co.jp. Retrieved on 2011-06-18.
^Samsø Labyrinten – verdens største labyrint Archived 22 April 2003 at the Wayback Machine. Samsolabyrinten.com. Retrieved on 2011-06-18.
^Google Maps. Maps.google.com.au (1970-01-01). Retrieved on 2011-06-18.
^Hortus Vitalis – Irrgarten und Erlebniswelt – Ausflugsziel in Bad Salzuflen Archived 13 August 2008 at the Wayback Machine. Hortus-vitalis.de. Retrieved on 2011-06-18.
^Labyrinth Park Archived 24 May 2017 at the Wayback Machine. Retrieved on 2017-04-26.
^Google Maps. Maps.google.com.au (1970-01-01). Retrieved on 2017-04-26.
^"Archived copy". Archived from the original on 21 April 2009. Retrieved 4 March 2009.CS1 maint: Archived copy as title (link)
^"Italian creates world's largest maze". 4 July 2010. Archived from the original on 12 March 2016.
^"Het Labyrinth". klausvandelocht.nl. Archived from the original on 2 October 2010.
^"Doolhof van Ruurlo – geschiedenis". Archived from the original on 1 August 2012.
^Jardins no Parque do Arnado Archived 30 September 2009 at the Wayback Machine. Ponte de Lima. Retrieved on 2011-06-18.
^C.M. Porto Archived 18 March 2009 at the Wayback Machine. Cm-porto.pt. Retrieved on 2011-06-18.
^Google Maps. Maps.google.com.au (1970-01-01). Retrieved on 2011-06-18.
^Reserva Florestal de Recreio do Pinhal da Paz (São Miguel) Archived 19 June 2012 at the Wayback Machine. Azores.gov.pt. Retrieved on 2011-06-18.
^"León cuenta con un laberinto único en el mundo. nortecastilla.es". www.elnortedecastilla.es.
^"Parc del Laberint d'Horta". Archived from the original on 4 February 2013.
^"Archived copy". Archived from the original on 12 June 2017. Retrieved 28 May 2017.CS1 maint: Archived copy as title (link)
^"Archived copy". Archived from the original on 8 October 2016. Retrieved 28 May 2017.CS1 maint: Archived copy as title (link)
^"Archived copy". Archived from the original on 12 June 2017. Retrieved 28 May 2017.CS1 maint: Archived copy as title (link)
^maze Archived 14 August 2006 at the Wayback Machine. Greatmaze.info. Retrieved on 2011-06-18.
^Google Maps. Maps.google.com.au (1970-01-01). Retrieved on 2011-06-18.
^"Carnfunnock Maze". Larne Borough Council. Archived from the original on 27 September 2011. Retrieved 5 August 2010.
^Records Search Page Archived 8 May 2006 at the Wayback Machine. Guinness World Records. Retrieved on 2011-06-18.
^Google Maps. Maps.google.com.au (1970-01-01). Retrieved on 2011-06-18.
^London's Labyrinths and Mazes Archived 21 November 2016 at the Wayback Machine Londonist. Retrieved on 2016-11-20.
^Glendurgan Garden Archived 20 May 2012 at the Wayback Machine. National Trust (2005-11-17). Retrieved on 2011-06-18.
^Palaces, Historic Royal. "Lose Yourself In The Famous, Fun-Filled Hampton Court Maze - Historic Royal Palaces". Archived from the original on 29 July 2012.
^"Mazes - Hever Castle". Archived from the original on 2 March 2012.
^Hoo Hill Maze Archived 20 December 2005 at the Wayback Machine. Wuff.me.uk. Retrieved on 2011-06-18.
^Google Maps. Maps.google.com.au (1970-01-01). Retrieved on 2011-06-18.
^Norwich Cathedral Labyrinth Archived 22 May 2013 at the Wayback Machine. Norwich Cathedral. Retrieved on 2012-04-04.
^The Maize Maze Archived 22 August 2006 at the Wayback Machine. Farmmaze.co.uk (2005-07-10). Retrieved on 2011-06-18.
^"Would yew enjoy maize?". Evening Chronicle. 19 January 2005. Retrieved 1 December 2012.
^Somerleyton Hall and Gardens Archived 28 March 2012 at the Wayback Machine. Somerleyton Estate. Retrieved on 2012-04-04.
^ abStarr, Michelle (14 July 2013). "Doctor Who celebrates with 18-acre Dalek corn maze". CNet. Archived from the original on 21 June 2015.
^York Maze website Archived 13 November 2014 at the Wayback Machine Retrieved 2014-13-11.
^Kooser, Amanda (11 September 2012). "World's largest QR code is a Canadian corn maze". CNet. Archived from the original on 21 June 2015.
^Kooser, Amanda (4 September 2013). "Navigate this massive corn maze using Google Street View". CNet.
^ abKooser, Amanda (9 January 2015). "'The Shining' hotel wants you to design a hedge maze for it". CNet. Archived from the original on 21 June 2015.
^ ab"'The Shining' Hotel to Finally Get a Real Hedge Maze". Construction Equipment Guide. 26 May 2015. Archived from the original on 27 May 2015.
^"Music in the Berkshires: Classical Beyond Tanglewood, Part 3". Hampton Terrace. Archived from the original on 10 July 2012. Retrieved 3 April 2011.
^"Maze". Chartwell Castle. Archived from the original on 24 October 2016. Retrieved 22 May 2017.
^WEBDE.COM.BR. "Município de Nova Petrópolis - Empresa". Archived from the original on 30 September 2011.
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
Look up maze in Wiktionary, the free dictionary.
Wikisource has the text of the 1911 Encyclopædia Britannica article maze.
Media related to Mazes at Wikimedia Commons
"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.
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Garden features
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Avenue
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