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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, but also can 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

Maze constructionEdit

 
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,[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 mazesEdit

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 mazesEdit

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 experimentsEdit

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

Other types of mazesEdit

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.

GalleryEdit

Publications about mazesEdit

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 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 publicEdit

AsiaEdit

DubaiEdit

JapanEdit

PacificEdit

New ZealandEdit

EuropeEdit

AustriaEdit

BelgiumEdit

DenmarkEdit

GermanyEdit

GreeceEdit

ItalyEdit

NetherlandsEdit

PortugalEdit

SpainEdit

UKEdit

North AmericaEdit

 
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

CanadaEdit

  • 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.[48][49]

USAEdit

South AfricaEdit

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.[53]

South AmericaEdit

BrazilEdit

  • Labirinto Verde,[54] Nova Petrópolis, (Circular hedge maze built in 1989; Latitude 29°22'32.71"S Longitude 51°06'43.68"W)

Mazes in popular cultureEdit

Fictional mazesEdit

See alsoEdit

ReferencesEdit

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  2. ^ Lappa Valley Steam Railway – 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 (2007-12-23). Retrieved on 2011-06-18.
  4. ^ de Ruiter, Johan (2017). Hamilton Mazes - The Beginner's Guide. 
  5. ^ Friedman, Erich (2009). "Hamiltonian Mazes". Erich's Puzzle Palace. Archived from the original on 16 April 2016. Retrieved 27 May 2017. 
  6. ^ Mazes, Vladimir Koziakin (Grosset & Dunlap, 1971) ISBN 0-448-01836-5
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  25. ^ 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.
  26. ^ http://www.elnortedecastilla.es/20080922/local/leon/leon-cuenta-laberinto-unico-200809221723.html
  27. ^ "Parc del Laberint d'Horta". Archived from the original on 4 February 2013. 
  28. ^ "Archived copy". Archived from the original on 12 June 2017. Retrieved 2017-05-28. 
  29. ^ "Archived copy". Archived from the original on 8 October 2016. Retrieved 2017-05-28. 
  30. ^ "Archived copy". Archived from the original on 12 June 2017. Retrieved 2017-05-28. 
  31. ^ maze Archived 14 August 2006 at the Wayback Machine.. Greatmaze.info. Retrieved on 2011-06-18.
  32. ^ Google Maps. Maps.google.com.au (1970-01-01). Retrieved on 2011-06-18.
  33. ^ "Carnfunnock Maze". Larne Borough Council. Archived from the original on 27 September 2011. Retrieved 5 August 2010. 
  34. ^ Records Search Page Archived 8 May 2006 at the Wayback Machine.. Guinness World Records. Retrieved on 2011-06-18.
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  47. ^ York Maze website Archived 13 November 2014 at the Wayback Machine. Retrieved 2014-13-11.
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  49. ^ Kooser, Amanda (4 September 2013). "Navigate this massive corn maze using Google Street View". CNet. 
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Further readingEdit

  • Abelson, H. & diSessa, A. (1980). Turtle Geometry: The Computer as a Medium for Exploring Mathematics. MIT Press. 
  • 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. 
  • 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.  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 linksEdit