Maze Explained

Maze should not be confused with Maize.

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.

Construction

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,^[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 also be built with snow.

Generation

See 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.

Solution

See 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]

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

Types

Ball-in-a-maze puzzles: Dexterity puzzles which involve navigating a ball through a maze or labyrinth.

Fractal maze: A maze containing holes inside which the maze is indefinitely repeated at a smaller scale.^[4]

Hamilton maze: A maze in which the goal is to find the unique Hamiltonian cycle.^{[5] [6]}

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

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

Public attractions

Asia

Dubai

• Gardens Shopping Mall, Dubai (world's largest indoor maze)^[7]

India

• Bhulbhulayia

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

Czech Republic

• Obludiste, Dolni Pena (Jindrichuv Hradec) - hedge maze 6.000 m²

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
• ,^[17] Chiusi, Tuscany (see Pliny's Italian labyrinth)
• Villa Pisani, Stra, near Venice (45.4096°N 12.0131°W)
• The labyrinth of Franco Maria Ricci at Fontanellato^[18] (44.854°N 10.1464°W)

Netherlands

• Waterlabyrinth, Nijmegen, designed by Klaus van de Locht, 1981^[19]
• Doolhof Ruurlo, Ruurlo, designed by Daniel Marot, based on the design for Hampton Court Maze^[20]

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]
• Parc de la Torreblanca, Esplugues de Llobregat
• 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

United Kingdom

• 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]
• Saffron Walden, an Essex town with its historic Bridge End Gardens hedge maze and the England's largest turf maze^[43]
• 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.^[44]
• Somerleyton Hall, Suffolk, England. A yew hedge maze designed and planted in 1846 by William Nesfield.^[45]
• Traquair House, Peeblesshire, Scotland. A beech tree hedge maze designed by John Schofield.^[46]
• York Maze, near RAF Elvington, with a different design each year

North America

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]}

United States

• The Stanley Hotel in Estes Park, Colorado in 2015 installed a 10,100-square-foot hedge maze on its front lawn, using 1,600 to 2,000 Alpine Currant hedge bushes. Previously the hotel had no maze, though one was featured prominently in the 1980 film adaption of Stephen King's novel The Shining, which is set at the hotel.
• Dole Pineapple Plantation, Oahu.
• Tanglewood Music Center Hedge Maze, Lenox and Stockbridge, Massachusetts.^[49]
• The Wooz was a maze attraction opened in 1988 in Vacaville, California by Sun Creative System, a Japanese company that had seen success with the concept in Japan. Despite initial interest, high admission cost and hot summers led the park to close in 1992. The failure of the Wooz scuttled Sun Creative System's plans for additional maze attractions in the U.S.^[50]

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.^[51]

Caribbean

Cuba

The colonial city of Camagüey, Cuba, founded in 1528, layout resembles a real maze, with narrow, short streets always turning in one direction or another. After pirate Henry Morgan burned the city in the 17th century, it was designed like a maze so attackers would find it hard to move around inside the city. It is a UNESCO World Heritage Site.

South America

Brazil

• Labirinto Verde,^[52] Nova Petrópolis, (Circular hedge maze built in 1989; Latitude 29°22'32.71"S Longitude 51°06'43.68"W)

In popular culture

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;^[53] on American Gladiators, both contestants ran through the maze simultaneously and were given 45 seconds to find the correct solution.^[54] The giant maze was part of the game rotation on both programs concurrently, and was also retired from both programs simultaneously.

The Shining

• The film adaptation of Stephen King's 1977 novel, The Shining (1980), includes a scene featuring Jack Torrance and Danny Torrance in a hedge maze.^{[55] [56]}

See also

• Celtic maze
• Stone labyrinths of Bolshoi Zayatsky Island
• Troy Town

Further reading

• Ettore Selli, "Labirinti Vegetali, la guida completa alle architetture verdi dei cinque continenti", Ed. Pendragon, 2020; ISBN 9788833642222
• Book: Abelson, H. . diSessa, A. . Turtle Geometry: The Computer as a Medium for Exploring Mathematics. registration . MIT Press . 1980. 9780262010634.
• Book: Fisher, Adrian . The Amazing Book of Mazes. registration . London: Thames & Hudson and New York: Harry N Abrams Inc. 2006. 978-0-500-51247-0.
• Book: Fisher, Adrian . Gerster, Georg . The Art of the Maze. Weidenfeld & Nicolson. London . 1990. 0-297-83027-9.
• Book: Fisher, Adrian . Loxton, Howard . amp . Secrets of the Maze. London. Thames & Hudson. 1997 . 978-0-500-01811-8.
• Book: Fisher, Adrian . Saward, Jeff . The British Maze Guide. Minotaur Designs. St Albans, UK . 1991. The definitive guide to British Mazes.
• Book: Martineau, John Southcliffe . Mazes and Labyrinths: In Great Britain. Wooden Books . 2005. 978-1-904263-33-3.
• Book: Matthews, W. H. . Mazes and Labyrinths: Their History and Development. 1927. Includes News: Bibliography. Mazes and Labyrinths. 1970. Dover Publications . 0-486-22614-X.
• Book: Saward, Jeff . Magical Paths. Mitchell Beazley . 2002. 1-84000-573-4.

External links

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

Notes and References

1. Book: Hermann Kern . Through the labyrinth: designs and meanings over 5000 years . 2000. Prestel . 978-3-7913-2144-8 . 23 . live . https://web.archive.org/web/20140101055608/http://books.google.com/books?id=pAFsQgAACAAJ . 1 January 2014 .
2. Web site: Trevithick Brick Path Maze . Lappa Valley Steam Railway . 13 June 2010 . live . https://web.archive.org/web/20090812061325/http://www.lappavalley.co.uk/maze.htm . 12 August 2009 .
3. https://www.youtube.com/watch?v=k1tSK5V1pds Maze to Tree
4. Web site: Fractal Maze - Wolfram Demonstrations Project.
5. Book: de Ruiter, Johan . 2017 . Hamilton Mazes - The Beginner's Guide.
6. Web site: Hamiltonian Mazes . Friedman . Erich . 2009 . Erich's Puzzle Palace . 27 May 2017 . dead . https://web.archive.org/web/20160416235225/http://www2.stetson.edu/~efriedma/puzzle/ham/ . 16 April 2016 .
7. http://www.ameinfo.com/45024.html Retail Arabia to open French hypermarket Géant in The Gardens Shopping Mall | Nakheel Properties
8. http://www.iwami.or.jp/hish/kankou/meiro/maze.htm welcome to hikimi town!!
9. http://www.kinugawa.ne.jp/facilities/palladium/palladium.html 巨大迷路パラディアム
10. http://www.hi-land.co.jp/ 仙台ハイランド ホームページ
11. http://www.royalpines.co.jp/shirahama/ ：：白浜エネルギーランド：： 移転連絡
12. http://www.samsolabyrinten.com/ Samsø Labyrinten – verdens største labyrint
13. http://maps.google.com.au/maps?ll=55.971925,10.551124 Google Maps
14. http://www.hortus-vitalis.de Hortus Vitalis – Irrgarten und Erlebniswelt – Ausflugsziel in Bad Salzuflen
15. http://www.labyrinthpark.gr/en Labyrinth Park
16. http://maps.google.com.au/maps?ll=35.2950336,25.357162 Google Maps
17. Web site: Nuova pagina 0 . 4 March 2009 . dead . https://web.archive.org/web/20090421201900/http://www.toscanaunderground.it/eng/labirintoporsenna.htm . 21 April 2009 .
18. Web site: Italian creates world's largest maze . . 4 July 2010 . live . https://web.archive.org/web/20160312172200/http://www.theguardian.com/world/2010/jul/04/world-largest-maze-italy . 12 March 2016 .
19. Web site: Het Labyrinth . klausvandelocht.nl . dead . https://web.archive.org/web/20101002054630/http://www.klausvandelocht.nl/het_labyrinth.htm . 2 October 2010 .
20. Web site: Doolhof van Ruurlo – geschiedenis. https://archive.today/20120801065658/http://www.doolhofruurlo.nl/geschiedenis.html. dead. 1 August 2012.
21. http://www.pontedelima.com/index.php?option=com_content&view=article&id=168:jardins-no-parque-do-arnado&catid=76:parques-e-jardins&Itemid=170 Jardins no Parque do Arnado
22. http://www.cm-porto.pt/gen.pl?p=stories&op=view&fokey=cmp.stories/2383 C.M. Porto
23. http://maps.google.com.au/maps?ll=41.158021,-8.587639 Google Maps
24. http://www.azores.gov.pt/Portal/pt/entidades/sraf-drrf/textoImagem/Pinhal+da+Paz.htm Reserva Florestal de Recreio do Pinhal da Paz (São Miguel)
25. Web site: León cuenta con un laberinto único en el mundo. nortecastilla.es. www.elnortedecastilla.es. 22 September 2008.
26. Web site: Parc del Laberint d'Horta . dead . https://web.archive.org/web/20130204003627/http://w110.bcn.cat/portal/site/MediAmbient/menuitem.0d4d06202ea41e13e9c5e9c5a2ef8a0c/?vgnextoid=2598b9255ea6a210VgnVCM10000074fea8c0RCRD&vgnextchannel=6de179583ad1a210VgnVCM10000074fea8c0RCRD&lang=en_GB . 4 February 2013 . 16 December 2012 .
27. Web site: Archived copy . 28 May 2017 . live . https://web.archive.org/web/20170612194810/http://laberintodevillapresente.es/ . 12 June 2017 .
28. Web site: Identificación . 28 May 2017 . live . https://web.archive.org/web/20161008173402/http://www.tentegorraventura.com/galeria-laberinto/ . 8 October 2016 .
29. Web site: Palacio Real de la Granja de San Ildefonso . 28 May 2017 . live . https://web.archive.org/web/20170612194811/http://www.patrimonionacional.es/real-sitio/palacio-real-de-la-granja-de-san-ildefonso . 12 June 2017 .
30. http://www.greatmaze.info/maze.html maze
31. http://maps.google.com.au/maps?ll=51.881823,0.474719 Google Maps
32. Web site: Carnfunnock Maze . Larne Borough Council . 5 August 2010 . dead . https://web.archive.org/web/20110927150600/http://www.larne.gov.uk/template1.asp?parent=588&parent2=646&pid=651&area=6&text=text%3D1 . 27 September 2011 .
33. http://www.guinnessworldrecords.com/content_pages/record.asp?recordid=47417 Records Search Page
34. http://maps.google.com.au/maps?ll=54.258284,-5.953174 Google Maps
35. http://londonist.com/2011/02/londons-labyrinths-and-mazes/ London's Labyrinths and Mazes
36. http://www.nationaltrust.org.uk/glendurgan-garden/ Glendurgan Garden
37. Web site: Lose Yourself in the Famous, Fun-Filled Hampton Court Maze - Historic Royal Palaces . Historic Royal . Palaces . dead . https://web.archive.org/web/20120729012841/http://www.hrp.org.uk/HamptonCourtPalace/maze . 29 July 2012 .
38. Web site: Mazes - Hever Castle . live . https://web.archive.org/web/20120302085055/http://www.hevercastle.co.uk/yew-maze.aspx . 2 March 2012 .
39. http://www.wuff.me.uk/hoo%20hill%20maze/noj.html Hoo Hill Maze
40. http://maps.google.com.au/maps?ll=52.029145,-0.321728 Google Maps
41. http://www.cathedral.org.uk/visitorinfo/the-labyrinth--the-labyrinth.aspx Norwich Cathedral Labyrinth
42. http://www.farmmaze.co.uk/ The Maize Maze
43. Web site: The Essex town where you can do five amazing outdoor mazes in a day. 18 February 2019.
44. Web site: Would yew enjoy maize?. Evening Chronicle. 19 January 2005. 1 December 2012.
45. http://www.somerleyton.co.uk/hallgardens/gardens_maze.php Somerleyton Hall and Gardens
46. Web site: The Traquair maze.
47. News: World's largest QR code is a Canadian corn maze . CNet . Kooser, Amanda . 11 September 2012 . live . https://web.archive.org/web/20150621031733/http://www.cnet.com/news/worlds-largest-qr-code-is-a-canadian-corn-maze/ . 21 June 2015 .
48. News: CNet . Kooser, Amanda . Navigate this massive corn maze using Google Street View . 4 September 2013.
49. Web site: Music in the Berkshires: Classical Beyond Tanglewood, Part 3. https://archive.today/20120710005047/http://hamptonterrace.com/wp/153/music-in-the-berkshires-classical-beyond-tanglewood-part-3/. dead. 10 July 2012. Hampton Terrace. 3 April 2011.
50. Web site: The history of the hottest, most ill-advised theme park ever made: The Wooz . Dowd . Katie . 2021-06-17 . sfgate.com . SFGATE . 2022-10-06 .
51. Web site: Maze . Chartwell Castle . 22 May 2017 . live . https://web.archive.org/web/20161024160214/http://chartwellcastle.co.za/maze.html . 24 October 2016 .
52. Web site: Município de Nova Petrópolis - Empresa . WEBDE.COM.BR . live . https://web.archive.org/web/20110930054630/http://www.novapetropolis.rs.gov.br/int_empresa.php?tipo=5&id=144 . 30 September 2011 .
53. https://www.youtube.com/watch?v=O43hZ3piBZQ A segment of an early 1992 episode of Nubeluz featuring the maze. The first player's turn begins at the top of the segment; the second player's turn begins at 5:20.
54. https://www.youtube.com/watch?v=IWB3x6rVmQw The maze featured on American Gladiators.
55. News: 'The Shining' hotel wants you to design a hedge maze for it . Kooser . Amanda . 9 January 2015 . CNet . live . https://web.archive.org/web/20150621014000/http://www.cnet.com/news/the-shining-hotel-wants-you-to-design-a-hedge-maze-for-it/ . 21 June 2015 .
56. News: Construction Equipment Guide . 'The Shining' Hotel to Finally Get a Real Hedge Maze . 26 May 2015 . live . https://web.archive.org/web/20150527015317/http://www.constructionequipmentguide.com/The-Shining-Hotel-to-Finally-Get-a-Real-Hedge-Maze/25381/ . 27 May 2015 .

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