Part of a series on |
Puzzles |
---|
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.
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 be built with snow.
Quality conventions for designing mazes differ according to the medium each maze is to be rendered in: Mazes to be walked by people should not reveal a closed end from a primary branch point, so that any person traversing the maze must walk further, in order to determine if a turn leads to a viable path. Mazes traced on paper typically use long, mostly parallel, convoluted routes, even for paths that are dead ends, so that a person tracing the maze has difficulty identifying dead ends while the pencil is set at a branch point.[ citation needed ]
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.
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 are often used in psychology experiments to study spatial navigation and learning. Such experiments typically use rats or mice. Examples are:
This section needs additional citations for verification .(January 2022) |
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.
India
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]
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.
In Greek mythology, the Labyrinth was an elaborate, confusing structure designed and built by the legendary artificer Daedalus for King Minos of Crete at Knossos. Its function was to hold the Minotaur, the monster eventually killed by the hero Theseus. Daedalus had so cunningly made the Labyrinth that he could barely escape it after he built it.
Transport puzzles are logistical puzzles, which often represent real-life transportation problems. The classic transport puzzle is the river crossing puzzle in which three objects are transported across a river one at time while avoiding leaving certain pairs of objects together. The term should not be confused with the usage of transport puzzle as a shortened form of transportation puzzle, representing children's puzzles with different transportation vehicles used as puzzle pieces.
Topiary is the horticultural practice of training perennial plants by clipping the foliage and twigs of trees, shrubs and subshrubs to develop and maintain clearly defined shapes, whether geometric or fanciful. The term also refers to plants which have been shaped in this way. As an art form it is a type of living sculpture. The word derives from the Latin word for an ornamental landscape gardener, topiarius, a creator of topia or "places", a Greek word that Romans also applied to fictive indoor landscapes executed in fresco.
Hampton Court Maze is a hedge maze at Hampton Court Palace and the oldest surviving hedge maze in Britain.
Longleat is an English stately home and the seat of the Marquesses of Bath. A leading and early example of the Elizabethan prodigy house, it is adjacent to the village of Horningsham and near the towns of Warminster and Westbury in Wiltshire, and Frome in Somerset.
Adrian Fisher is a British pioneer, inventor, designer and creator of mazes, puzzles, public art, tessellations, tilings, patterns and networks of many kinds. He is responsible for more than 700 mazes in 42 countries since 1979.
Historically, a turf maze is a labyrinth made by cutting a convoluted path into a level area of short grass, turf or lawn. Some had names such as Mizmaze, Troy Town, The Walls of Troy, Julian's Bower, or Shepherd's Race. This is the type of maze referred to by William Shakespeare in A Midsummer Night's Dream when Titania says:
Mizmaze is the name given to two of England's eight surviving historic turf mazes, and also to a third, presumably once similar site that is now merely a relic. Of the two which survive, one is at Breamore, in Hampshire; the other is on top of St Catherine's Hill, overlooking the city of Winchester, Hampshire.
Packwood House is a timber-framed Tudor manor house in Packwood on the Solihull border near Lapworth, Warwickshire. Owned by the National Trust since 1941, the house is a Grade I listed building. It has a wealth of tapestries and fine furniture, and is known for the garden of yews.
A picture maze is a maze puzzle designed to resemble something visually, or one where the solution traces out a particular picture.
Gilbert Randoll Coate was a British diplomat, maze designer and "labyrinthologist".
A hedge maze is an outdoor garden maze or labyrinth in which the "walls" or dividers between passages are made of vertical hedges.
A corn maze or maize maze is a maze cut out of a corn field. Originally, the first full-size corn maze was believed to be created in Annville, Pennsylvania in 1993; however, similar corn mazes were highlighted in newspapers as early as 1982. Corn mazes have become popular tourist attractions in North America, and are a way for farms to generate tourist income. Many are based on artistic designs such as characters from movies. Corn mazes appear in many different designs. Some mazes are even created to tell stories or to portray a particular theme. Most have a path which goes all around the whole pattern, either to end in the middle or to come back out again, with various false trails diverging from the main path. In the United Kingdom, they are known as maize mazes, and are especially popular with farms in the east of England. These mazes are normally combined with other farm attractions of interest to families and day trippers. Some of these attractions include hay rides, a petting zoo, play areas for children, and picnic areas. Each year a few of the mazes are featured in national newspapers and TV. In the U.S., corn mazes typically are cut down circa the first week of November; in the UK typically in September after children return to school.
Uncle Henry's Playhouse is the third game in The 7th Guest series. Functionally the game is a compilation game mostly composed of the puzzles from Trilobyte's games The 7th Guest, The 11th Hour, and Clandestiny, but featuring little plot. The game has been noted for its low sales figures and its rarity/obscurity relative to its blockbuster predecessors, The 7th Guest and The 11th Hour. The game is primarily intended as a means of presenting puzzles from the previous titles in the 7th Guest series and consequently it has a rather simplistic plot that has been criticized by reviewers for its thinness in comparison to the previous games. The game also includes previews for two then-upcoming Trilobyte games, Tender Loving Care and Dog Eat Dog.
Finca Los Alamos is a historical Argentine estancia located in San Rafael, Mendoza. The estate was built in 1830 by the Bombal family, and originally served as a frontier fort. Domingo Bombal, who served eleven terms as Governor to the Mendoza Province, owned the estate until his death in 1908.
Maize, also known as corn in North American and Australian English, is a cereal grain first domesticated by indigenous peoples in southern Mexico about 10,000 years ago. The leafy stalk of the plant gives rise to inflorescences which produce pollen and separate ovuliferous inflorescences called ears that when fertilized yield kernels or seeds, which are botanical fruits. The term maize is preferred in formal, scientific, and international usage as the common name because this refers specifically to this one grain whereas corn refers to any principal cereal crop cultivated in a country. For example, in North America and Australia corn is often used for maize, but in England and Wales it can refer to wheat or barley, and in Scotland and Ireland to oats.
Dave Phillips is a maze and puzzle designer, and writer of The Zen Of The Labyrinth—Mazes For The Connoisseur. Phillips has provided puzzles for Reader's Digest, Highlights, National Geographic World, Die Zeit, Ranger Rick, Omni, Games, Scientific American, and United Features Syndicate. He has also created jigsaw puzzle mazes for Hallmark and die cut puzzle mazes for DaMert.
The labyrinth of Versailles was a hedge maze in the Gardens of Versailles with groups of fountains and sculptures depicting Aesop's fables. André Le Nôtre initially planned a maze of unadorned paths in 1665, but in 1669, Charles Perrault advised Louis XIV to include thirty-nine fountains, each representing one of the fables of Aesop. The work was carried out between 1672 and 1677. Water jets spurting from the animals mouths were conceived to give the impression of speech between the creatures. There was a plaque with a caption and a quatrain written by the poet Isaac de Benserade next to each fountain. A detailed description of the labyrinth, its fables and sculptures is given in Perrault's Labyrinte de Versailles, illustrated with engravings by Sébastien Leclerc.
Bridge End Gardens is a group of linked ornamental gardens in Saffron Walden, Essex, England. The gardens are listed Grade II* on the Register of Parks and Gardens. They are located off Castle Street, close to the Fry Art Gallery. Features include a maze.
A formal garden is a garden with a clear structure, geometric shapes and in most cases a symmetrical layout. Its origin goes back to the gardens which are located in the desert areas of Western Asia and are protected by walls. The style of a formal garden is reflected in the Persian gardens of Iran, and the monastic gardens from the Late Middle Ages. It has found its continuation in the Italian Renaissance gardens and has culminated in the French formal gardens from the Baroque period. Through its design, the garden conveys a sense of established order and transparency to the observer.
{{cite web}}
: CS1 maint: archived copy as title (link){{cite web}}
: CS1 maint: url-status (link)