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Obludiste - hedge maze Czech republic

A hedge maze at Longleat stately home in England

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.[ citation needed]

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.[ citation needed]

A small maze with one entrance and one exit. This is an example of a fair design for a walking maze, but a poor design for a paper-tracing maze.

Generation

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.[ citation needed]

Solution

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.[ citation needed]

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:

Types

A fractal maze (top) with 3 iterations (left) and a solution (right)
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

Publications

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, [7] 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. [8] 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.

Public attractions

Asia

Dubai

India

Japan

Pacific

New Zealand

Europe

Austria

Belgium

Czech republic

Denmark

Germany

Greece

Italy

Netherlands

Portugal

Spain

United Kingdom

Traquair House Maze, Scotland

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. [49] [50]

United States

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. [56]

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, [57] 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; [58] on American Gladiators, both contestants ran through the maze simultaneously and were given 45 seconds to find the correct solution. [59] The giant maze was part of the game rotation on both programs concurrently, and was also retired from both programs simultaneously.

The Shining

See also

References

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  2. ^ "Trevithick Brick Path Maze". Lappa Valley Steam Railway. Archived from the original on 12 August 2009. Retrieved 13 June 2010.
  3. ^ Maze to Tree Archived 12 April 2016 at the Wayback Machine. YouTube (23 December 2007). Retrieved on 18 June 2011.
  4. ^ "Fractal Maze - Wolfram Demonstrations Project".
  5. ^ de Ruiter, Johan (2017). Hamilton Mazes - The Beginner's Guide.
  6. ^ Friedman, Erich (2009). "Hamiltonian Mazes". Erich's Puzzle Palace. Archived from the original on 16 April 2016. Retrieved 27 May 2017.
  7. ^ Mazes, Vladimir Koziakin (Grosset & Dunlap, 1971) ISBN  0-448-01836-5
  8. ^ Twilley, Nicola (18 November 2021). "How the World's Foremost Maze-Maker Leads People Astray". The New Yorker. Retrieved 7 September 2022.
  9. ^ 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 18 June 2011.
  10. ^ welcome to hikimi town!! Archived 13 July 2008 at the Wayback Machine. Iwami.or.jp. Retrieved on 18 June 2011.
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  12. ^ 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 18 June 2011.
  13. ^ ::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 18 June 2011.
  14. ^ Samsø Labyrinten – verdens største labyrint Archived 22 April 2003 at the Wayback Machine. Samsolabyrinten.com. Retrieved on 18 June 2011.
  15. ^ Google Maps. Maps.google.com.au (1 January 1970). Retrieved on 18 June 2011.
  16. ^ Hortus Vitalis – Irrgarten und Erlebniswelt – Ausflugsziel in Bad Salzuflen Archived 13 August 2008 at the Wayback Machine. Hortus-vitalis.de. Retrieved on 18 June 2011.
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  18. ^ Google Maps. Maps.google.com.au (1 January 1970). Retrieved on 26 April 2017.
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  27. ^ "León cuenta con un laberinto único en el mundo. nortecastilla.es". www.elnortedecastilla.es. 22 September 2008.
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  29. ^ "Archived copy". Archived from the original on 12 June 2017. Retrieved 28 May 2017.{{ cite web}}: CS1 maint: archived copy as title ( link)
  30. ^ "Identificación". Archived from the original on 8 October 2016. Retrieved 28 May 2017.
  31. ^ "Palacio Real de la Granja de San Ildefonso". Archived from the original on 12 June 2017. Retrieved 28 May 2017.
  32. ^ maze Archived 14 August 2006 at the Wayback Machine. Greatmaze.info. Retrieved on 18 June 2011.
  33. ^ Google Maps. Maps.google.com.au (1 January 1970). Retrieved on 18 June 2011.
  34. ^ "Carnfunnock Maze". Larne Borough Council. Archived from the original on 27 September 2011. Retrieved 5 August 2010.
  35. ^ Records Search Page Archived 8 May 2006 at the Wayback Machine. Guinness World Records. Retrieved on 18 June 2011.
  36. ^ Google Maps. Maps.google.com.au (1 January 1970). Retrieved on 18 June 2011.
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  38. ^ Glendurgan Garden Archived 20 May 2012 at the Wayback Machine. National Trust (17 November 2005). Retrieved on 18 June 2011.
  39. ^ Palaces, Historic Royal. "Lose Yourself in the Famous, Fun-Filled Hampton Court Maze - Historic Royal Palaces". Archived from the original on 29 July 2012.
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  43. ^ Norwich Cathedral Labyrinth Archived 22 May 2013 at the Wayback Machine. Norwich Cathedral. Retrieved on 4 April 2012.
  44. ^ The Maize Maze Archived 22 August 2006 at the Wayback Machine. Farmmaze.co.uk (10 July 2005). Retrieved on 18 June 2011.
  45. ^ "The Essex town where you can do five amazing outdoor mazes in a day". 18 February 2019.
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  47. ^ Somerleyton Hall and Gardens Archived 28 March 2012 at the Wayback Machine. Somerleyton Estate. Retrieved on 4 April 2012.
  48. ^ "The Traquair maze".
  49. ^ Kooser, Amanda (11 September 2012). "World's largest QR code is a Canadian corn maze". CNet. Archived from the original on 21 June 2015.
  50. ^ Kooser, Amanda (4 September 2013). "Navigate this massive corn maze using Google Street View". CNet.
  51. ^ a b Kooser, 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.
  52. ^ a b "'The Shining' Hotel to Finally Get a Real Hedge Maze". Construction Equipment Guide. 26 May 2015. Archived from the original on 27 May 2015.
  53. ^ "Music in the Berkshires: Classical Beyond Tanglewood, Part 3". Hampton Terrace. Archived from the original on 10 July 2012. Retrieved 3 April 2011.
  54. ^ "I Entered A Renaissance Festival Maze". Sir Guy of Warwick.
  55. ^ Dowd, Katie (17 June 2021). "The history of the hottest, most ill-advised theme park ever made: The Wooz". sfgate.com. SFGATE. Retrieved 6 October 2022.
  56. ^ "Maze". Chartwell Castle. Archived from the original on 24 October 2016. Retrieved 22 May 2017.
  57. ^ WEBDE.COM.BR. "Município de Nova Petrópolis - Empresa". Archived from the original on 30 September 2011.
  58. ^ 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.
  59. ^ https://www.youtube.com/watch?v=IWB3x6rVmQw The maze featured on American Gladiators.

Further reading

External links