Maze

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A maze is a 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, as the labyrinth has a single through-route with twists and turns but without branches, and is not designed to be as difficult to navigate.[1] The pathways and walls in a maze or labyrinth are fixed (pre-determined) – puzzles where the walls and paths can change during the game are categorised as tour puzzles. The Cretan labyrinth is the oldest known maze.[2]

Contents

Maze construction

Mazes have been built with walls and rooms, with hedges, turf, corn stalks, hay bales,cheese, potatos,old shoes books, paving stones of contrasting colors or designs, bricks and turf,[3] 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

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, 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

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.[4]

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

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.
Ball-in-a-maze puzzles
Dexterity puzzles which involve navigating a ball through a maze or labyrinth.
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,[5] 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.[6]
  • Walkabout Mazes and Botanical Gardens,[7] Robertson, Western Cape, South Africa. 13870 m² net area Google Maps[8]

Asia

India

Dubai

  • Gardens Shopping Mall, Dubai (World's Largest Indoor Maze)[9]

Japan

Oceania

Australia

New Zealand

  • The Great Maze, The Puzzling World,[20] Wanaka, South Island (1.5 km of passages)

Europe

Austria

Public hedge maze in the "English Garden" at Schönbusch Park, Aschaffenburg, Germany
The labyrinth of Barvaux, Durbuy
Inside the labyrinth of Villa Pisani

Germany

Greece

Italy

Portugal

Scandinavia

Spain

UK

North America

Public maze at Wild Adventures theme park, Valdosta, Georgia. It was removed before the 2010 season.
Maze at Missouri Botanical Garden in St. Louis

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 978-0-500-51247-0
  • Adrian Fisher, Armchair Puzzlers: Mad Mazes, University Books, San Francisco, USA (2005) ISBN 978-1-57528-978-6
  • Adrian Fisher, Mazes and Follies, Jarrold Publishing, UK (2004) ISBN 978-1-84165-142-2
  • Adrian Fisher, Mazes and Labyrinths, Shire Publications, UK (2003) ISBN 978-0-7478-0561-8
  • Adrian Fisher and Howard Loxton, Secrets of the Maze, Thames & Hudson, London (1997) / Barron’s Educational Series Inc, New York (1998) ISBN 978-0-500-01811-8
  • 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 978-0-517-58099-8
  • W. H. Matthews, Mazes and Labyrinths: Their History and Development[62] (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

  1. ^ Kern, Through the Labyrinth, p. 23.
  2. ^ AMS.org
  3. ^ Lappa Valley Steam Railway - Trevithick Brick Path Maze, Lappa Valley Steam Railway, http://www.lappavalley.co.uk/maze.htm, retrieved 13 June 2010 
  4. ^ Youtube.com
  5. ^ Mazes, Vladimir Koziakin (Grosset & Dunlap, 1971) ISBN 0-448-01836-5
  6. ^ Google Maps
  7. ^ Soekershof Soekershof.com
  8. ^ Google.com.au
  9. ^ Ameinfo.com
  10. ^ Iwami.or.jp
  11. ^ Kisomura.com
  12. ^ Kinugawa.ne.jp
  13. ^ Hi-land.co.jp
  14. ^ Royalpines.co.jp
  15. ^ Google Maps
  16. ^ Google Maps
  17. ^ Google Maps
  18. ^ Amazenthings.com.au
  19. ^ Google Maps
  20. ^ Puzzlingworld.co.nz
  21. ^ Google Maps
  22. ^ Google Maps
  23. ^ Hortus-vitalis.de
  24. ^ Toscanaunderground.it
  25. ^ CM-porto.pt
  26. ^ Google Maps
  27. ^ Pontedelima.com
  28. ^ Azores.gov.pt
  29. ^ Google Maps
  30. ^ Samsolabyrinten.com
  31. ^ Google Maps
  32. ^ Google Maps
  33. ^ Google Maps
  34. ^ Greatmaze.info
  35. ^ Google Maps
  36. ^ Google Maps
  37. ^ Google Maps (hard to see)
  38. ^ Guinessworldrecords.com
  39. ^ Google Maps
  40. ^ Google Maps
  41. ^ Google Maps
  42. ^ Google Maps
  43. ^ Google Maps
  44. ^ ME.uk
  45. ^ Google Maps
  46. ^ Google Maps
  47. ^ Google Maps
  48. ^ Google Maps
  49. ^ Google Maps
  50. ^ Farmmaze.co.uk
  51. ^ Google Maps
  52. ^ Google Maps
  53. ^ Google Maps
  54. ^ Amazingchicago.com
  55. ^ Severscornmaze.com
  56. ^ Davisfarmland.com
  57. ^ Dole-plantation.com
  58. ^ Labyrintheduhangar16.com
  59. ^ Mazefunpark.com
  60. ^ McMaze.ca
  61. ^ Trailofterrorfest.com
  62. ^ Sacred-texts.com

External links

Retrieved from "http://en.wikipedia.org/wiki/Maze"