Quadrant Model of Reality Book 7 Art and Philosophy

Flight formation aerobatics are flown by teams of up to sixteen aircraft, although most teams fly between four and ten aircraft. 16 is the squares of the quadrant model

The "Finger-four" formation (also known as the "four finger formation"), is a flight formation used by fighter aircraft. It consists of four aircraft, and four of these formations can be combined into a squadron formation. The formation consists of a flight of four aircraft, composed of a "lead element" and a "second element", each of two aircraft. When viewing the formation from above, the positions of the planes resemble the tips of the four fingers of a human right hand (without the thumb), giving the formation its name. Four Finger Formation.png Four Finger Squadron.PNG The lead element is made up of the flight leader at the very front of the formation and one wingman to his rear left. The second element is made up of an additional two planes, the element leader and his wingman. The element leader is to the right and rear of the flight leader, followed by the element wingman to his right and rear. Both the flight leader and element leader have offensive roles, in that they are the ones to open fire on enemy aircraft while the flight remains intact. Their wingmen have a defensive role — the flight wingman covers the rear of the second element and the element wingman covers the rear of the element lead. Four of these flights can be assembled to form a squadron formation which consists of two staggered lines of fighters, one in front of the other. Each flight is usually designated by a color (i.e. Red, Blue, Yellow, and Green). A squadron formation is 16 squares. That is the squares of the quadrant model.

The formation was developed by several air forces independently in the 1930s. The Finnish Air Force adopted it during 1934-1935.[1] [2] Luftwaffe pilots developed the formation independently in 1938 during the Spanish Civil War, and were the first to use it in combat. Most notable in its development and use in the Luftwaffe were Günther Lützow and Werner Mölders and their fellow airmen. In the German Luftwaffe the flight (German: Schwarm) was made up of two pairs (German: Rotte) of aircraft. Each Rotte was composed of a leader and a wingman. The aircraft in the Schwarm had greater vertical and horizontal separation, so they were free to scan in all directions for enemy aircraft rather than focusing on maintaining a close formation. This allowed the pilots to maintain greater situational awareness and reduce the chance of being spotted by the enemy due to the looser formation. The two Rotten could split up at any time and attack on their own. The Rottenführer (pair leader) would attack enemy aircraft, leaving his wingman to scan for threats and protect him while he engaged the enemy. The Finnish Air Force's approach was even more flexible by allowing the pilot who spotted the enemy to become the leader of the pair or even the whole flight for the duration of the attack as he had the best situational awareness at that moment in time. The Luftwaffe continued the use of this formation during the Battle of Britain, in which its effectiveness was shown to be considerably greater than the standard three-aircraft "Vic" close formation used by the Royal Air Force (RAF).[citation needed] The RAF and later the United States Army Air Forces (USAAF) and Soviet Air Forces adopted this formation and used it themselves against the Luftwaffe.[citation needed] The Finnish Air Force proved the effectiveness by achieving a 16:1 kill ratio with the finger-four during the 1939-1940 Winter War against the Soviet Air Force, which at the time used the conventional Vic formation and superior aircraft.[citation needed] The Soviet air force units in the Spanish Civil War adopted the formation against the Germans but reverted to the "V" on return to the Soviet Union. The flying ace Douglas Bader was the first RAF pilot to adopt the formation in 1940. The United States Army Air Corps and Naval Aviation began using a concept called "Fighting Pair" from 1940–41. Japan too adopted the finger-four formation during World War II.[3][4][5] Missing man formation Main article: Missing man formation The finger-four formation became less common after World War II. However, it is still used in the "Missing Man Formation" at pilots' funeral ceremonies. The formation performs a fly-by in level flight over the funeral, at which point the second element leader climbs vertically and departs the formation, symbolizing the departure of the person being honored.

At the outbreak of the Second World War the Vic was still in use by both bombers and fighter formations in most air forces; however the German air forces fighter units had changed to the more flexible and aggressive pair (Rotte) and four (Schwarm) combination. These comprised a pair (leader and wingman) and four (two pairs) in a “finger-four” arrangement

The missing man formation is an aerial salute performed as part of a flypast of aircraft at a funeral or memorial event, typically in memory of a fallen pilot.[1][2] The formation is often called the "missing man flyby" or "flypast".[3] Several variants of the formation are seen. The formation most commonly used in the United States is based on the “finger-four” aircraft combat formation composed of a pair of two-aircraft elements.[4] The aircraft fly in a V-shape with the flight leader at the point and his wingman on his left. The second element leader and his wingman fly to his right. The formation flies over the ceremony low enough to be clearly seen and the second element leader abruptly pulls up out of the formation while the rest of the formation continues in level flight until all aircraft are out of sight. In an older variant the formation is flown with the second element leader position conspicuously empty. In another variation, the flight approaches from the south, preferably near sundown, and one of the aircraft will suddenly split off to the west, flying into the sunset. In all cases, the aircraft performing the pull-up, split off, or missing from the formation, is honoring the person (or persons) who has died, and it represents their departure to the heavens. In the movie Hell Divers from 1932, the closing flyby shows a missing man formation. U.S. Navy F/A-18 jets fly a missing man formation at a memorial service for astronaut Neil Armstrong on 31 August 2012. In 1936, King George V received the first recorded flypast for a non-RAF funeral. The United States adopted the tradition in 1938 during the funeral for Major General Oscar Westover with over 50 aircraft and one blank file.[3] By the end of World War II, the missing man formation had evolved to include the pull-up. In April 1954, United States Air Force General Hoyt Vandenberg was buried at Arlington National Cemetery without the traditional horse-drawn artillery caisson. Instead, Vandenberg was honored by a flyover of jet aircraft with one plane missing from the formation. On November 26, 1999, four Air Force F-16s flew the missing man formation over Kyle Field to honor the 12 Aggies who died during the Aggie Bonfire collapse.[5] The Delaware Air National Guard flew the missing man formation over the Dover International Speedway on June 3, 2001 to honor NASCAR driver Dale Earnhardt Sr., who had perished in a wreck on the final lap of the 2001 Daytona 500 race on February 18. In December 2004, as a final tribute to Prince Bernhard of the Netherlands's former military role in the Royal Netherlands Air Force, three modern F-16 jet fighters and a World War II Spitfire performed a missing man formation during his funeral. The missing man formation was flown at a family memorial service in Indian Hill, Ohio on 31 August 2012 in honour of former American astronaut, US Navy pilot, and test pilot Neil Armstrong, the first man to walk on the Moon. In November 2014 the state memorial service for former Australian Prime Minister Gough Whitlam, who had served as a navigator in the Royal Australian Air Force during World War II, concluded with a missing man formation flight conducted by four RAAF F/A-18 Hornet fighters.[6] On 29 March 2015, the Republic of Singapore Air Force's Black Knights attempted to fly the missing man formation as an aerial salute to long-serving Prime Minister Lee Kuan Yew during his funeral procession from Parliament House to the University Cultural Centre of the National University of Singapore, but was unable to do so, due to poor weather conditions. [7] [8] Motorsport variant The missing man formation is also used in various types of motorsport to commemorate the death of a driver, rider, or official.[9] In case of a rolling start, during the pace laps before the race begins, the driver in the pole position drops back a row into the second row and the field paces with no vehicle in the lead position.[10] Similarly, the pole position on a starting grid can be left empty for a standing start. In drag racing, the variant of the missing man formation only is put into place if a driver has lost his/her life sometime before the race but after having qualified. Should that happen, the deceased driver's lane remains vacant for what would have been his/her quarterfinal race and the opposing driver, who must cross the finish line without being disqualified in order to proceed, will slowly drive their car (referred to as "idling") down the track as a sign of respect for the fallen opponent (a recent example occurring when Robert Hight did this in honor of Scott Kalitta, who was killed in a qualifying crash in 2008). Rolling Honor Guard variant The missing man formation is also used for the motorcycle Rolling Honor Guards. A common formation of motorcycles is five in front of the hearse: two motorcycles in tandem (#1 and #2, left and right, from the perspective of the hearse), two motorcycles directly in front of the hearse, in tandem (#5 and #6, left and right, as noted), and a solo rider in the resultant #4 position, and the missing motorcycle (in the #3 position) representing the fallen. This is performed for both the loss of a person who was a member of the motorcycle club/organization, or, may be provided as a sign of respect by groups such as the Patriot Guard Riders.

The thach weave when the planes cross, making a sort of quadrant with their movment. In the Battle of Midway it was done by four planes. The Thach Weave (also known as a Beam Defense Position) is an aerial combat tactic developed by naval aviator John S. Thach of the United States Navy soon after the United States' entry into World War II. Thach had heard, from a report published in the 22 September 1941 Fleet Air Tactical Unit Intelligence Bulletin, of the Japanese Mitsubishi Zero's extraordinary maneuverability and climb rate. Before even experiencing it for himself, he began to devise tactics meant to give the slower-turning American F4F Wildcat fighters a chance in combat. While based in San Diego, he would spend every evening thinking of different tactics that could overcome the Zero's maneuverability, and would then test them in flight the following day.[citation needed] Working at night with matchsticks on the table, he eventually came up with what he called "Beam Defense Position", but which soon became known as the "Thach Weave". It was executed either by two fighter aircraft side-by-side or by two pairs of fighters flying together. When an enemy aircraft chose one fighter as his target (the "bait" fighter; his wingman being the "hook"), the two wingmen turned in towards each other. After crossing paths, and once their separation was great enough, they would then repeat the exercise, again turning in towards each other, bringing the enemy plane into the hook's sights. A correctly executed Thach Weave (assuming the bait was taken and followed) left little chance of escape to even the most maneuverable opponent. The basic Thach Weave, executed by two wingmen. Thach called on Ensign Edward "Butch" O'Hare, who led the second section in Thach's division, to test the idea. Thach took off with three other Wildcats in the role of defenders, Butch O'Hare meanwhile led four Wildcats in the role of attackers. The defending aircraft had their throttles wired (to restrict their performance), while the attacking aircraft had their engine power unrestricted - this simulated an attack by superior fighter aircraft.[1] Trying a series of mock attacks, Butch found that in every instance Thach's fighters, despite their power handicap, had either ruined his attack or actually maneuvered into position to shoot back. After landing, Butch excitedly congratulated Thach: "Skipper, it really worked. I couldn't make any attack without seeing the nose of one of your airplanes pointed at me." Thach carried out the first test of the tactic in combat during the Battle of Midway in June 1942, when a squadron of Zeroes attacked his flight of four Wildcats. Thach's wingman, Ensign R. A. M. Dibb, was attacked by a Japanese pilot and turned towards Thach, who dove under his wingman and fired at the incoming enemy aircraft's belly until its engine ignited. The maneuver soon became standard among US Navy pilots and was adopted by USAAF pilots. Marines flying Wildcats from Henderson Field on Guadalcanal also adopted the Thach Weave. The tactic initially confounded the Japanese Zero pilots flying out of Rabaul. Saburō Sakai, the famous Japanese ace, relates their reaction to the Thach Weave when they encountered Guadalcanal Wildcats using it:[2] For the first time Lt. Commander Tadashi Nakajima encountered what was to become a famous double-team maneuver on the part of the enemy. Two Wildcats jumped on the commander's plane. He had no trouble in getting on the tail of an enemy fighter, but never had a chance to fire before the Grumman's team-mate roared at him from the side. Nakajima was raging when he got back to Rabaul; he had been forced to dive and run for safety. The maneuver proved so effective that American pilots also used it during the Vietnam War, and it remains an applicable tactic as of 2013.[3]

Mouse in the maze was another video game made in 1959. These prototype video games were extraordinarily simple. It basically involved a dot moving through a maze but the maze was extremely simple, merely a quadrant grid

Space War was also one of the first 1950 video game prototypes. The game could not be played on a regular computer but needed to be played on a University campus computer so it could never be marketed. It involved two players trying to fight each other in space around a sun. Player controls include clockwise and counterclockwise rotation, thrust, fire, and hyperspace. Initially these were controlled using the front-panel test switches, with four switches for each player, but these proved to wear out very quickly under normal gameplay, and the location of the switches left one player off to one side of the CRT display and visually disadvantaged as a result.[3] Most sites used custom control boxes wired into the same switches, although joysticks and other inputs were also used. Four optional features were controlled by sense switches on the console: no star (and thus no gravity) enable angular momentum disable background starfield the "Winds of Space"- a warping factor on trajectories that require the pilot to make careful adjustments every time they move.

Tennis For Two was an electronic game developed in 1958 on a Donner Model 30 analog computer, which simulates a game of tennis or ping pong on an oscilloscope. Created by American physicist William Higinbotham for visitors at the Brookhaven National Laboratory, it is important in the history of video games as one of the first electronic games to use a graphical display. Tennis for two was probably the second video game ever created. It was played on a screen that looked like a quadrant grid

In 1952, Alexander S. Douglas created OXO, a software program for the Electronic Delay Storage Automatic Calculator (EDSAC) computer, which simulates a game of tic-tac-toe. The EDSAC was the first computer to have memrory that could be read from or written to, and filled an entire room; it included three 35×16 dot matrix cathode ray tubes to graphically display the state of the computer's memory.[9][18] As a part of a thesis on human–computer interaction, Douglas used one of these screens to portray other information to the user; he chose to do so via displaying the current state of a game.[19] The player entered input using a rotary telephone controller, selecting which of the nine squares on the board they wished to move next. Their move would appear on the screen, and then the computer's move would follow.[20] The game was not available to the general public, and was only available to be played in the University of Cambridge's Mathematical Laboratory, by special permission, as the EDSAC could not be moved.[21] Like other early video games, after serving Douglas's purpose, the game was discarded.[9] Around the same time, Strachey expanded his draughts program for another mainframe computer, the Manchester Mark 1, culminating in a version for the Ferranti Mark 1 in 1952, which had a CRT display.[22] Like OXO, the display was mostly static, updating only when a move was made.[23] OXO and Strachey's draughts program are the earliest known games to display visuals on an electronic screen. Again, the genesis of video games was tic tac toe, checkers, and chess, all games made up of quadrants.

The first publicly demonstrated electronic game was created in 1950. Bertie the Brain was an arcade game of tic-tac-toe, built by Dr. Josef Kates for the 1950 Canadian National Exhibition. As I mentioned tic tac toe is made up of quadrants Around this time, non-visual games were being developed at various research computer laboratories; for example, Christopher Strachey developed a simulation of the game draughts, or checkers, for the Pilot ACE that he unsuccessfully attempted to run for the first time in July 1951 at the British National Physical Laboratory and completed in 1952; this is the first known computer game to be created for a general-purpose computer, rather than a machine specifically made for the game like Bertie. Checkers was the second video game created, also made of quadrants

The Legend of Zelda: A Link to the Past and Four Swords[a] is an action-adventure game co-developed by Nintendo and Capcom and published by Nintendo for the Game Boy Advance. It is the ninth installment in the The Legend of Zelda video game series. There are always four Link characters (differentiated by different colors: green, red, blue and purple) in play, regardless of the number of people playing; "extra" Links are attached to those directly controlled and positioned around the controlling character. Normally, the extra Links follow the player, but players can separate an individual Link and control independently, or put the four Links into formations. These techniques are required to solve puzzles and defeat enemies. Players are encouraged to work together to gather enough Force Gems to empower the Four Sword, and failing to do so by the time the boss is defeated or the dark barrier is reached results in having to go back to the beginning of the stage to collect more. However, once the requisite gems are collected, players are automatically transported to the dark barrier and therefore do not have to repeat the entire stage. The Links eventually save the shrine maidens, retrieve the Dark Mirror, destroy Shadow Link and Vaati, and face Ganon in an ultimate showdown. The Links defeats Ganon and seal him firmly in the Four Sword. Peace returns to Hyrule and the people celebrate as all traces of the evil that plagued Hyrule are vanquished.[3] Link then returns the Four Sword back to its resting pedestal and the Four Links become one again. The nature of the quadrant model is there are four quadrants but they are really all one. Zelda is one of the most popular video games of all time.

The Legend of Zelda: The Minish Cap (/ˈmɪnɪʃ/) (Japanese: ゼルダの伝説 ふしぎのぼうし Hepburn: Zeruda no Densetsu: Fushigi no Bōshi?, lit. The Legend of Zelda: The Mysterious Cap) is an action-adventure game and the twelfth entry in the The Legend of Zelda series. Developed by Capcom, with Nintendo overseeing the development process, it was released for the Game Boy Advance handheld game console in Japan and Europe in 2004 and in North America and Australia the following year.[1] In this story Link retrieves the four elemental artifacts and uses them to restore the Picori Blade to the Four Sword,[11] capable of defeating Vaati. The sign of zelda is the sierpinsky triangle which I described is four triangles, one within the other three, which is the quadrant pattern in its essence.

In the Legend of Zelda: Majora's Mask,The gameplay is centered on the perpetually repeating three-day cycle and the use of various masks, some of which allow Link to transform into different beings. Link learns to play several melodies on his ocarina, which have a variety of effects like controlling the flow of time or opening passages to four temples, which house challenges Link must overcome Link has three masks that can transform him into different forms. So he has four forms. His three transformations receive different reactions from non-player characters.[10] For instance, the Goron and Zora are allowed to exit Clock Town at will, whereas the Deku Scrub is not permitted to leave by reason of his childlike resemblance. Animals also interact differently with the four forms of Link. The Legend of Zelda: Majora's Mask is set in Termina, a land parallel to Hyrule,[18][19] the latter being the main setting of most games in the series. According to legend, Termina was split into four areas by four magical giants that live in four regions of the land. At the center of Termina lies Clock Town, which features a large clock tower that counts down the days before the Carnival of Time—a major festival where the people of Termina pray for good luck and harvests. Termina Field surrounds Clock Town; beyond lie a swamp, mountain range, bay, and canyon in each of the four cardinal directions. Link must then travel between the four cardinal regions of Termina: Woodfall, Snowhead, the Great Bay, and Ikana Canyon, for each region conceals one of the Four Giants who will be able, once reunited, to halt the moon's crashing. At the same time, each region has been struck with a terrible curse by the Skull Kid which plagues its inhabitants and seals away its giant. To lift the curse and free the giants, Link must enter a dungeon in each region and defeat its boss. After doing so, he obtains the power to summon the giant he has set free. With all four curses lifted, Link climbs on top of the Clock Tower at midnight on the third day to confront the Skull Kid again. There and then, he summons the Four Giants, who halt the moon's descent toward Termina by holding it up with their arms. Now seeing the Skull Kid as a useless puppet, Majora's Mask drops his grip on him and flies up to possess the moon instead. With Tatl at his side, Link follows the Majora's Mask inside the moon and defeats him once and for all, returning the moon to its proper place in the sky.[22] The Four Giants return to their sleep. Tatl and Tael reunite with the newly liberated Skull Kid. The Happy Mask Salesman takes Majora's Mask, stating it has been purified of its evil power. Link rides away on Epona while the people of Termina celebrate the Carnival of Time and the dawn of a new day. The game ends with a post-credits scene depicting Link and Epona back in the mysterious forest, resuming Link's search for his friend, as they ride off towards a mysterious light breaking through the thick forest. A drawing on a tree stump of Link, Tatl, Tael, the Skull Kid, and the Four Giants is shown after. Notice the repetition of fours.

In Zelda II: The Adventure of Link, Link begins the game with four Heart Containers and four Magic Containers and can acquire up to four more of each, permanently increasing his life points and magic points respectively.

As I mentioned, Zelda is one of the most popular video games of all time. I do not think it is a coincidence that the games portray the quadrant four a lot. In Oracle of Seasons, the environment changes with the four seasons. From spring, summer, winter, autumn. Gameplay is sometimes affected by the seasons; during the winter for example, a path opens up that cannot be accessed during any other season; or during spring, the flower can be used to access unreachable ledges. The central item of Oracle of Seasons is the Rod of Seasons. By standing on a stump and swinging the rod, Link can change the season and affect his surroundings.[20] For example, to cross a body of water, Link can change the season to winter and walk on the ice. Changing the season to summer causes vines to flourish, which Link can use to scale cliffs. When Link obtains the rod, he initially cannot use it.[21] In the course of the game, Link visits four towers that house the four spirits of the seasons; each tower Link visits allows him to switch to an additional season.[21]

In Zelda there are four Light Spirits (光の精霊 Hikari no Seirei?) throughout Hyrule. All of the light spirits are found in Twilight Princess. The first light spirit is Ordona (ラトアーヌ Ratoānu?), best described as an Ordon Goat. Ordona has a spiraling circular orb in between her antlers and first appears at Ordon Spring. She appears once Link has defeated the first Shadow Beast. The second light spirit, Faron (フィローネ Firōne?), is described as a monkey/ape. He is holding his golden orb with his tail eclipsed over his head. He appears in Faron Spring, and will fully appear when Link has completed the first collection of twilight bugs. The third light spirit, Eldin (オルディン Orudin?), is described as an eagle, with his orb between his feet. He appears in the lake near the shaman's house in Kakariko Village, and will fully appear once Link has completed the second collection of twilight bugs. The fourth and last light spirit, Lanayru (ラネール Ranēru?), is described as a serpent, with his orb inside his mouth. He appears in the cave at Lake Hylia. He fully appears when Link has completed the third and final collection of twilight bugs. But once Link is back to his human form, and after Lanayru tells him the story of the three goddesses and the three Fused Shadows, Zant appears. Zant will then embed the Shadow Crystal in Link's skull that will allow Link to transform into his human and wolf form. He will also expose Midna to Lanayru, causing her to become very ill, and sending Link on the quest for the Master Sword.

In Zelda the Deku (デクナッツ Dekunattsu?) are a race of plant-like creatures which are introduced in Ocarina of Time. They appear mostly in the overworld and dungeons. Deku are generally short and have leaves sprouting out from their heads. They often have red, glowing eyes, and their mouths are short, hollow tubes that can shoot "Deku Nuts". Their bodies consist entirely of wood and leaves, and they perish quickly if set on fire. They can fly by using large leaves to glide, and some can use the leaves on their head to fly for indefinite periods after taking off from a "Deku Flower." There are four types of Deku depicted in the series: Deku Scrubs, Mad Scrubs, Business Scrubs, and Royal Scrubs. Deku Scrubs are the most common type, which have green leaves. They often give information when caught. Mad Scrubs are violent, have red and yellow leaves, and do not talk. Business Scrubs are traders who offer to sell their wares and services. Royal Scrubs have larger heads, bigger eyes, smaller mouths, and they also have extra leaves covering their body. In The Legend of Zelda: Majora's Mask, Link can inhabit the body of an unknown Deku Scrub (who is heavily implied to be the son of the Deku King's butler) and can fly for a limited time with use of a Deku Flower and can shoot bubbles from its mouth (once he receives the magic meter from the Great Fairy). The Deku Scrub cannot go into deep water but hops on top of it five times and then sinks.

Tetra is princess Zelda In Zelda the princess's name is Tetra. Tetra means four. Tetra's name could be derived from the Ancient Greek word meaning "four," similar to Tetris. It could also be derived from an actual Tetra, a type of South American freshwater fish, adding to the sea-faring theme of the game. Tetra could also allude to tetrahedron, the physical shape of the Triforce. (the sierpinski triangle, the triangle with four triangles within it) In The Wind Waker Tetra is the leader of the pirates. When Link first meets Tetra, she is being kidnapped by the Helmaroc King. The monster bird is distracted by Tetra's crew and she is dropped into the Fairy Woods. Link comes to her rescue, but because of this distraction, his sister Aryll, mistaken for Tetra, is kidnapped instead.

Berzerk was one of the original video games made in 1980. Again there are four enemies in this game with the fourth being different than the other three. There are three colors of robots, and then there is the fourth evil otto, the nemesis of the humanoid protagonist. It is a very simple game where the player can move the four directions up and down and left and right kind of in a quadrant manner.

Dark yellow robots that do not fire

Red robots that can fire 1 bullet (500 points)

Dark cyan robots that can fire 2 bullets (1,500 points)

In this version of the game, after 5,000 points, Evil Otto doubles his speed, moving as fast as the player while robots remain in the maze, and twice as fast as the player after all the robots are destroyed.

In the sitcom My Name is Earl (Season 1, Episode 8), the character "Crabman" is portrayed, playing Berzerk and scoring high. He afterwards would take a polaroid photograph of the screen, pinning the highscore to his personal wall of fame.[20]

In the Futurama episode "Fear of a Bot Planet", the Anti-Human Patrol robots, along with the PA loudspeaker, use the sound samples of "Get the humanoid!" and "Intruder alert! Intruder alert!" from the original game.[21] The episode "Anthology of Interest II" features an actual robot from the game, and the spoken line of the robot references the style of the sound samples ("Fork 'em over! FORK 'EM OVER!").[22]

In The Simpsons episode "Homer Goes to College", Homer visits some nerds who mutter "Intruder alert" and "Stop the humanoid".[23]

In the NewsRadio episode "Rosebowl", news director Dave Nelson introduces an unpopular new employee evaluation system. In the fracas following the adoption of this new system, Dave is referred to as "Evil Otto" by the two news anchors, Bill McNeal and Catherine Duke.[24]

In the popular online game World of Warcraft, Gnomish Alarm-O-Bots call out "Intruder Alert!" when attacked in the same robotic voice as Evil Otto.

Donkey Kong Jr. (ドンキーコングJR. Donkī Kongu Junia?) is a 1982 arcade-style platform video game by Nintendo. It first appeared in arcades, and, over the course of the 1980s, was later released for a variety of platforms, most notably the Nintendo Entertainment System. The game's title is written out as Donkey Kong Junior in the North American arcade version and various ports to non-Nintendo systems. Its eponymous star, Donkey Kong Jr., also called simply Junior[3] or abbreviated as DK Jr.,[4] is trying to rescue his father Donkey Kong, who has been imprisoned. Donkey Kong's cage is guarded by Mario, in his only appearance as an antagonist in a Nintendo video game. This game is the sequel to the video game Donkey Kong, which featured Mario as the hero and Junior's father as the villain (while in this game, it's the other way around). Like its predecessor, Donkey Kong, Jr. is an arcade-style platform game. There are a total of four stages, each with a unique theme. DK Jr. can run left and right, jump, and grab vines/chains/ropes to climb higher on the screen. He can slide down faster by holding only one vine, or climb faster by holding two. Enemies include "Snapjaws," which resemble bear traps with eyes, bird-like creatures called "Nitpickers", and "Sparks" that roam across the wiring in one of Mario's hideouts. To pass the first three stages, DK Jr. must reach the key at the top. In the fourth stage, DK Jr. must push six keys into locks near the top of the stage to free Donkey Kong. After a brief cutscene, the player is taken back to the first stage at an increased difficulty. DK Jr. loses a life when he touches any enemy or projectile, falls too great a distance, or falls off the bottom of the screen. Additionally, he loses a life if the timer counts down to zero. The game ends when the player loses all of his or her lives The first three stages are different than the fourth. This is the nature of the quadrant model. The original games Mario and Donkey Kong, which remained the most popular video games throughout video game history, started reflecting completely the quadrant model pattern.

Lemmings was a later 1991 video game. But it was divided into four difficulty categories. So it was not one fo the original prototypes that really reflected the quadrant model. Lemmings is divided into a number of levels, grouped into four difficulty categories.[1] Each level begins with a trap door opening from above, releasing a steady line of lemmings who all follow each other.[2] Levels include a variety of obstacles that prevent lemmings from reaching the exit, such as large drops, booby traps and pools of lava. The four difficulty groups – "Fun", "Tricky", "Taxing" and "Mayhem" – are used to organize the levels to reflect their overall difficulty.[7] This rating reflects several factors, including the number of obstacles the player has to surpass, the limitation on the number of types of skills available to assign, the time limit, the minimum rate of lemming release, and the percentage of lemmings that must be saved.[5]

Minecraft is a very popular video game. The game primarily consists of four game modes: survival, creative, adventure, and spectator. It also has a changeable difficulty system of four levels; the easiest difficulty (peaceful) removes any hostile creatures that spawn.[34] Survival mode The Minecraft crafting screen, showing the crafting pattern of two stone axes In this mode, players have to gather natural resources (such as wood and stone) found in the environment in order to craft certain blocks and items.[22] Depending on the difficulty, monsters spawn in darker areas in a certain radius of the character, requiring the player to build a shelter at night.[22] The mode also features a health bar which is depleted by attacks from monsters, falls, drowning, falling into lava, suffocation, starvation, and other events. Players also have a hunger bar, which must be periodically refilled by eating food in-game, except in "Peaceful" difficulty, in which the hunger bar does not drain. If the hunger bar is depleted, automatic healing will stop and eventually health will deplete. Health replenishes when players have a nearly full hunger bar, and also regenerates regardless of fullness if players play on the easiest difficulty. There are a wide variety of items that players can craft in Minecraft.[35] Players can craft armor, which can help mitigate damage from attacks, while weapons such as swords can be crafted to kill enemies and other animals more easily. Players may acquire resources to craft tools, such as axes, shovels, or pickaxes, used to chop down trees, dig soil, and mine ores, respectively; tools made of iron perform their tasks more quickly than tools made of stone or wood and can be used more heavily before they break. Players may also trade goods with villager mobs through a bartering system involving trading emeralds for different goods.[36] Villagers often trade with emeralds, wheat or other materials.[25][36] The game has an inventory system, and players can carry a limited number of items. Upon dying, items in the players' inventories are dropped, and players re-spawn at the current spawn point, which is set by default where players begin the game, but can be reset if players sleep in a bed.[37] Dropped items can be recovered if players can reach them before they despawn. Players may acquire experience points by killing mobs and other players, mining, smelting ores, breeding animals, and cooking food. Experience can then be spent on enchanting tools, armor and weapons.[34] Enchanted items are generally more powerful, last longer, or have other special effects.[34] Players may also play in hardcore mode, this being a variant of survival mode that differs primarily in the game being locked to the hardest gameplay setting as well as featuring permadeath; upon players' death, their world is deleted.[38] Creative mode An example of a creation constructed in Minecraft In creative mode, players have access to all of the resources and items in the game through the inventory menu, and can place or remove them instantly.[39] Players, who are able to fly freely around the game world, do not take environmental or mob damage, and are not affected by hunger.[40][41] The game mode helps players focus on building and creating large projects.[39] Adventure mode Adventure mode was added to Minecraft in version 1.3; it was designed specifically so that players could experience user crafted custom maps and adventures.[42][43][44] Gameplay is similar to survival mode but introduces various player restrictions, which can be applied to the game world by the creator of the map. This is so that players can obtain the required items and experience adventures in the way that the mapmaker intended.[44] Another addition designed for custom maps is the command block; this block allows mapmakers to expand interactions with players through certain server commands.[45] Spectator mode Spectator mode allows players to fly around through blocks and watch game play without interacting. In this mode, the inventory becomes a menu that allows the player to teleport to players in the world. It is also possible to view from the point of view of another player or creature. Some things may look different from another creature's point of view.

The TurboGrafx-16 Entertainment SuperSystem, known in Japan and in France as the PC Engine (PCエンジン Pī Shī Enjin?), is a home video game console joint-developed by Hudson Soft and NEC, released in Japan on October 30, 1987, in the United States on August 29, 1989, and in France on November 22, 1989. It was the first console released in the 16-bit era, albeit still utilizing an 8-bit CPU. Originally intended to compete with the Nintendo Entertainment System (NES), it ended up competing against the Mega Drive/Genesis, and later on the Super Famicom/Super NES. The TurboGrafx-16 has an 8-bit CPU and a dual 16-bit GPU. 16 is the number of squares in the quadrant model.

Bomberman is example of another original video game that was played within a visual quadrant grid with four possible directions, up, down, left, or right. Although it was not one of the 1970s original games.

Although Lumines is not one of the original video games from which the others spawned, it still reflects the quadrant model image. It is one of the most popular arcade games and puzzle of all time with tetris, which also reflects the quadrant pattern Lumines is a block-dropping game that may seem at first to be similar to Columns and Tetris. A 2x2 square (an O tetromino/ quadrant) made of four smaller block pieces is dropped into the playing field, which may appear different as the player advances through levels or skins. The small blocks that comprise the larger blocks will be one of two different colors. The objective is to rotate and align the blocks in such a way as to create 2x2 squares of the same color, which may span multiple blocks and, indeed, share blocks. For example, if one should get a 2x3 area of matching blocks, the middle portion will "share" itself with both the left and right halves and create two 2x2 squares. After the "timeline", which is synchronized to the music, sweeps over the matching blocks, they disappear. When too many unmatched blocks pile up to the point where no more blocks may be dropped in the playing field, the game ends. When part of a falling block hits an obstruction, the unobstructed portion of the block will split off and continue to fall. More points are scored by creating the largest number of squares during one "timeline" sweep. Increasing score multipliers are earned by repeatedly clearing squares on consecutive timeline sweeps. Bonuses are also awarded by reducing all remaining tiles to one single color or for removing all non-active tiles from the screen altogether. Occasionally, a block falls with a special square of one of the two colors with a "jewel" in the center. This square, when cleared as part of a matched 2x2 square, will cause all individual blocks of the same color that are horizontally or vertically adjacent to the matched 2x2 square, or to an adjacent square, to be cleared without score. These can be used for both generating large bonuses, since generally several blocks of the other color will be formed once these are removed, as well as to help the player recover if the field becomes too cluttered. There are four basic modes in the game: Challenge, Time Attack, Puzzle, Vs., and Vs. CPU Mode. Challenge Mode cycles through skins in a fixed order of generally increasing difficulty, and is played until the blocks pile up to the top of the screen. The maximum score in Challenge Mode is 999,999 points. Time Attack games give the player a limited time to clear as many blocks as possible. Puzzle mode challenges the player to create pictures (such as a cat, dog, cross, etc.) by forming the picture with one color while surrounding it with the opposite color. Vs. CPU mode is a series of battles against A.I. opponents. A line splits the playing field in half, and deleting blocks or combinations of blocks shifts the line towards the opposing player, giving the opposing player less room on their side. The battle ends when blocks pile up all the way to the top of the screen for one player. Two players with PSPs can use their wireless connection to play in the same way.

Whac-A-Mole is a popular arcade redemption game invented in 1976 by Aaron Fechter of Creative Engineering, Inc.. In Japan, もぐら退治 (mogura taiji, "Mole Buster") is a popular arcade game invented in 1975 by Kazuo Yamada of TOGO, based on ten of the designer's pencil sketches from 1974, licensed to Bandai in 1977.[1] ) It can also be commonly found at Japanese festivals. Whac-A-Mole arcade games originally had four holes in a quadrant formation out of which a mole would emerge and you had to hit it on the had. Later more holes were added

Skee ball was another very popular game played at arcades. It involved rolling a ball on a ramp where it would fly into holes. Traditional skee ball machines like this one do not include the two additional "100 points" holes, located on the uppermost corners of the machine, on either side of the "50 points" hole. Traditional skee ball had four scoring options. You could score 10 points by rolling the ball into the large first loop. You could get 30 by the second which was smaller. You could get 40 points by getting it in the hole above that. You get 50 points by getting it in the fourth highest hole. The fourth hole was different from the previous three because the previous three holes were encircled by the 10 point hole. The fourth square is always transcendent.

Pinball was a very popular game and had at most four flippers. The flippers in pinball are one or more small mechanically or electromechanically controlled levers, roughly 3 to 7 cm in length, used for redirecting the ball up the playfield. They are the main control that the player has over the ball. Careful timing and positional control allows the player to intentionally direct the ball in a range of directions with various levels of velocity. With the flippers, the player attempts to move the ball to hit various types of scoring targets, and to keep the ball from disappearing off the bottom of the playfield. The very first pinball games appeared in the early 1930s and did not have flippers; after launch the ball simply proceeded down the playfield, directed by static nails (or "pins") to one of several scoring areas. (These pins gave the game its name.) In 1947, the first mechanical flippers appeared on Gottlieb's Humpty Dumpty[23] and by the early 1950s, the familiar two-flipper configuration, with the flippers at the bottom of the playfield above the center drain, had become standard. Some machines also added a third or fourth flipper midway up the playfield. The new flipper ushered in the "golden age" of pinball, where the fierce competition between the various pinball manufacturers led to constant innovation in the field. Various types of stationary and moving targets were added, spinning scoring reels replaced games featuring static scores lit from behind. Multiplayer scores were added soon after, and then bells and other noise-makers, all of which began to make pinball less a game and more of an experience. The flippers have loaned pinball its common name in many languages, where the game is known mainly as "flipper".

TV Basketball of 1974 was the first sprite game. It involved four players in one line in two dimensions playing basketball

The players usually count aloud to 3, or speak the name of the game (e.g. "Rock Paper Scissors!" or "Ro Sham Bo!"), each time either raising one hand in a fist and swinging it down on the count or holding it behind. On the fourth count (saying, "Shoot!" or "Sho!"), the players change their hands into one of three gestures, which they then "throw" by extending it towards their opponent. Variations include a version where players use only three counts before throwing their gesture (thus throwing on the count of "Scissors!" or "Bo!"), or a version where they shake their hands three times before "throwing." There are usually three choices, rock paper or scissors. But occasionally a fourth is added. The fourth is always transcendent. Sometimes a fifth is added. The fourth always points to the fifth.

Literature

We categorize sentences into four main types, depending on the number and type of clauses they contain: Simple Sentence It has one independent clause. We drove from Connecticut to Tennessee in one day. Compound Sentence It has one more than one independent clause We were exhausted, but we arrived in time for my father's birthday party. Complex Sentence It has one independent clause and at least one or more dependent clause Although he is now 79 years old, he still claims to be 65. Compound-complex Sentence It has one more than one independent clause and at least one dependent clause The types are elucidated by a auadrant woth two axes Dichotomy one is one dependent vlause or many dependent clauses. Dichotomy 2 is one independent claise or many independent clauses. This yields four types

In September 1982, Arcade Express reviewed the ColecoVision port and scored Donkey Kong 9 out of 10.[33] Computer and Video Games reviewed the ColecoVision port in its September 1984 issue and scored it 4 out of 4 in all four categories of Action, Graphics, Addiction and Theme.[34]

Donkey Kong (Japanese: ドンキーコング Hepburn: Donkī Kongu?) is an arcade game released by Nintendo in 1981. It is an early example of the platform game genre, as the gameplay focuses on maneuvering the main character across a series of platforms while dodging and jumping over obstacles. In the game, Mario (originally named Mr. Video but then changed to "Jumpman") must rescue adamsel in distress named Pauline (originally named Lady), from a giant ape named Donkey Kong. The hero and ape later became two of Nintendo's most popular and recognizable characters. Donkey Kong is one of the most important titles from the Golden Age of Video Arcade Games, and is one of the most popular arcade games of all time. The game is divided into four different single-screen stages. Each represents 25 meters of the structure Donkey Kong has climbed, one stage being 25 meters higher than the previous. The final stage occurs at 100 meters. Stage one involves Mario scaling a construction site made of crooked girders and ladders while jumping over or hammering barrels and oil barrels tossed by Donkey Kong. Stage two involves climbing a five-story structure of conveyor belts, each of which transports cement pans. The third stage involves the player riding elevators while avoiding bouncing springs. The final stage involves Mario removing eight rivets which support Donkey Kong. Removing the final rivet causes Donkey Kong to fall and the hero to be reunited with Pauline.[16] These four stages combine to form a level. Upon completion of the fourth stage, the level then increments, and the game repeats the stages with progressive difficulty. For example, Donkey Kong begins to hurl barrels faster and sometimes diagonally, and fireballs get speedier. The victory music alternates between levels 1 and 2. The 22nd level is colloquially known as the kill screen, due to an error in the game's programming that kills Mario after a few seconds, effectively ending the game. Miyamoto then thought of using sloped platforms, barrels and ladders. When he specified that the game would have multiple stages, the four-man programming team complained that he was essentially asking them to make the game repeatedly.[19]:38–39 Nevertheless, they followed Miyamoto's design, creating a total of approximately 20 kilobytes of content.[20]:530 Yukio Kaneoka composed a simplistic soundtrack to serve as background music for the levels and story events.[

Mario Bros. (マリオブラザーズ Mario Burazāzu?) is a platform game published and developed for arcades by Nintendo in 1983. It was created by Shigeru Miyamoto. The player gains points by defeating multiple enemies consecutively and can participate in a bonus round to gain more points. Enemies are defeated by kicking them over once they have been flipped on their back. This is accomplished by hitting the platform the enemy is on directly beneath them. If the player allows too much time to pass after doing this, the enemy will flip itself back over, changing in color and increasing speed. Each phase has a certain number of enemies, with the final enemy immediately changing color and increasing its speed. There are four enemies: Square 1: the Shellcreeper, which simply walks around; Square 2: the Sidestepper, which requires two hits to flip over; Square 3: the Fighter Fly, which moves by jumping and can only be flipped when it is touching a platform; and Square 4: the Slipice, which turns platforms into slippery ice. When bumped from below, the Slipice dies immediately instead of flipping over. The original versions of Mario Bros.—the arcade version and the Family Computer/Nintendo Entertainment System (FC/NES) version—were received positively by critics.

Donkey Kong spawned the sequels Donkey Kong Jr. and Donkey Kong 3, as well as the spin-off Mario Bros. A complete remake of the original arcade game on the Game Boy, named Donkey Kong or Donkey Kong '94 contains levels from both the original Donkey Kong and Donkey Kong Jr arcades. It starts with the same damsel-in-distress premise and four basic locations as the arcade game and then progresses to 97 additional puzzle-based levels. It is the first game to have built-in enhancement for the Super Game Boy accessory. The arcade version makes an appearance in Donkey Kong 64 in the Frantic Factory level.

In the history of computer and video games, the fourth generation (more commonly referred to as the 16-bit era) of games consoles began on October 30, 1987 with the Japanese release of Nippon Electric Company's (NEC) PC Engine (known as the TurboGrafx-16 in North America). Although NEC released the first fourth generation console, and was second to the SNES in Japan, this era's sales were mostly dominated by the rivalry between Nintendo and Sega's consoles in North America: the Super Nintendo Entertainment System (the Super Famicom in Japan) and the Mega Drive (named the Sega Genesis in North America due to trademark issues). Nintendo was able to capitalize on its previous success in the third generation and managed to win the largest worldwide market share in the fourth generation as well. Sega was extremely successful in this generation and began a new franchise, Sonic the Hedgehog, to compete with Nintendo's Mario series of games. Several other companies released consoles in this generation, but none of them were widely successful. Nevertheless, several other companies started to take notice of the maturing video game industry and began making plans to release consoles of their own in the future. This generation ended with the Super Nintendo Entertainment System's discontinuation in 1999 in North America, Australia and Europe.[citation needed] 16 is the squares in the quadrant model

In The Legend of Zelda: Spirit Tracks Zelda demands to know how to prevent the Demon King's return, to which Anjean replies that the Spirit Tracks have to be restored by retrieving and completing several ancient rail maps (one for each of the four realms of Hyrule) from the above floors of the Tower to restore the Spirit Tracks. Then, the Tower must be linked up by the Spirit Tracks to four different temples, one in each of the four known realms.

In street fighter there is the final four boss opponents. These bosses I think are known as the Four Grand Masters.

In Metroid 4 there are four space pirate bosses In Metroid Prime, unlike those in earlier games in the series, the beam weapons in Metroid Prime have no stacking ability, in which the traits of each beam merge. Instead, the player must cycle the four beam weapons; there are charge combos with radically different effects for each

In most video games throughout the history of video games since advanced consoles like nintendo 64, four players engage in play using a split screen. The split screen looks like a quadrant.

Pong (marketed as PONG) is one of the earliest arcade video games and the very first sports arcade video game. It is a tennis sports game featuring simple two-dimensional graphics.

Bushnell felt the best way to compete against imitators was to create better products, leading Atari to produce sequels in the years followings the original's release: Pong Doubles, Super Pong, Ultra Pong, Quadrapong, and Pin-Pong.[3] The sequels feature similar graphics, but include new gameplay elements; for example, Pong Doubles allows four players to compete in pairs, while Quadrapong has them compete against each other in a four way field. There is no five way pong. The forth square is always different. The fifth is always questionable.

Space invaders was also the first game where players were given multiple lives,[64] had to repel hordes of enemies,[18] could take cover from enemy fire, and use destructible barriers,[65] in addition to being the first game to use a continuous background soundtrack, with four simple diatonic descending bass notes repeating in a loop, which was dynamic and changed pace during stages,[66] like a heartbeat sound that increases pace as enemies approached.[67] Whereas videogame music prior to Space Invaders was restricted to the extremities (i.e., a short introductory theme with game-over counterpart), the alien-inspired hit featured continuous music—the well-known four-note loop—throughout, uninterrupted by sound effects. "It was thus the first time that sound effects and music were superimposed to form a rich sonic landscape. Not only do players receive feedback related directly to their actions through sound effects; they also receive stimulus in a more subtle, non-interactive fashion through music

In each level of the original space invaders arcade game there were four types of enemies in each level. Each enemy type afforded a different amount of points. The fourth type afforded often a mystery amount of points (and it was a lot). The fourth is always transcendent.

Also in the original Space invaders video games there were four barriers that could protect your ship from enemy missiles.

Galaxy Wars is an arcade video game developed by Universal and manufactured by Taito in 1979. Gameplay[edit] Galaxy Wars Arcade game screen shot There are four parts to the game after getting through a certain number of levels. They are Good, Very Good, Wonderful and Fantastic. Depress the fire button for a missile. The missile speed increases when depressing the fire button continuously. Guide the missile from a stationary launch pad to the top of the screen to blow up the invading fleet of armed UFOs while dodging meteorites and bombs. Points are awarded for blowing up various ships and range from 50-550 depending on the ship. There is a bonus chance of 600 points for one pattern. After clearing a level or "pattern" as the back of the flyer calls it, the player was rewarded with messages like "Good!!" after 3 screens cleared, "Very Good!!" after 7 screens cleared, "Wonderful!!" after 10 screens cleared, and "Fantastic!!" after 15 screens cleared. Players who failed to score any points were told to "Give Up!!" A launcher appears every 3,000 additional points (5,000 if the adjustment is made in the controlling dip switches in the arcade cabinet). The game has a 1up and 2up player score and High Score tallied at the top of the screen. The arcade cabinet has one joystick to move the launcher left to right and guide the missiles.

Galaxians was another video game with the same type of schematic where there would be four types of enemies, and each level of enemy would give you a higher amount of points if killed. The fourth type would give a huge amount of points. The fourth is always transcendent.

Asteroids was another one of the original late 70's video games. It too had four iterations of enemies. There were large asteroids, that broke into medium asteroids, that broke into small asteroids. And then there was the space ship. The transcendent fourth. These video games began the video game revolution, and it is from them all of the other video games emerged.

Metroid: Other M, which takes place between Super Metroid and Fusion, provides more information about Samus's backstory and her emotional connection to both the Metroid hatchling and her former commander, Adam Malkovich, as well as her relation to all four Mother Brain designs, namely Zebes' Mother Brains, Aurora Unit 313 and MB.[16] Mother Brain (Japanese: マザーブレイン?) is a fictional character created by Nintendo for the Metroid series. She is one of the most prominent antagonists within the series, serving as the main antagonist of Metroid and Super Metroid.

Sea Wolf was one of the first video games. It featured a 1,2,3,4 on the screen. The light would cycle through 1,2,3,4 and then the gun would reload.

Tank uses a black and white Motorola television for its display.[3] The control panel consists of four military-style joysticks, two per player, with a fire button mounted on top of the right joystick of each pair

In 2010 a series of four classic Atari game CD-ROMs (Centipede, Lunar Lander, Super Breakout and Asteroids) were given away in kids' meals, and were also available for purchase separately

Atari's breakout was another one of the original video games out of which all video games emerged. Breakout is an arcade game developed and published by Atari, Inc.[2] It was conceptualized by Nolan Bushnell and Steve Bristow, influenced by the 1972 Atari arcade game Pong, and built by Steve Wozniak aided by Steve Jobs. The premise of the game was to break through four colors of blocks. The colors were yellow, red, blue and green. The red blocks make the balls go faster than the yellow blocks. The blue are faster than the red. The green are the fastest and make the ball go extremely fast. The fourth square is always transcendent.

Nibbler was a later game than the first 1970s games, but it was still an elementary early video game. It involved a snake moving through a maze that was based around a quadrant grid.

Snake was another popular elemental video game put on mobile phones. It involves a snake moving a possible four directions up down right or left. Its coordinates were centered around a quadrant orientation. Blockade was the prototype 1970s video game it grew out of. Blockade had four directional buttons.

007 was a very popular game in Nintendo 64. GoldenEye 007 is a first-person shooter video game developed by Rare and based on the 1995 James Bond film GoldenEye. It was exclusively released for the Nintendo 64 video game console in August 1997. The game features a single-player campaign in which players assume the role of British Secret Intelligence Service agent James Bond as he fights to prevent a criminal syndicate from using a satellite weapon against London to cause a global financial meltdown. The game also includes a split-screen multiplayer mode in which two, three, or four players can compete in different types of deathmatch games. The screen was usually split into four screens, forming a quadrant image. Diddy Kong racing was another game that was usually split into four screens as four friends would race each other

Gran Trak 10 is a single-player racing arcade game released by Atari in 1974. In the game, the player races against the clock with the intent of accumulating as many points as possible. Primitive diode-based ROM was used to store the sprites for the car, score and game timer, and the race track. The game's controls — steering wheel, four-position gear shifter, and accelerator and brake foot pedals — were also all firsts for arcade games. Steve Wozniak famously played Gran Trak 10 during the four-day development of a prototype for another Atari game, Breakout.[1]

Battle the Midway was an early video game that involved you using cross hairs of your periscope to shoot ships. The cross hairs looked like a quadrant. The game was basically a quadrant aiming at ships

Virtua Racing or V.R. for short, is a Formula One racing arcade game, developed by Sega AM2 and released in 1992. It was revolutionary because when selecting a car, the player can choose different transmission types.[3] VR introduced the "V.R. View System" by allowing the player to choose one of four views to play the game. This feature was then used in most other Sega arcade racing games (and is mentioned as a feature in the attract mode of games such as Daytona USA). It was later ported to home consoles, starting with the Mega Drive/Genesis in 1994.

Kwirk, known in Japan as Puzzle Boy (パズルボーイ?), is an action/transport puzzle video game first developed and published by Atlus in Japan on November 24, 1989 for the original Game Boy. In each room, Kwirk must navigate around and interact with various four obstacles in order to progress. Obstacles: Brick Walls – Cannot be moved nor walked through. Brick walls must be maneuvered around and blocks must be pushed around them. Turnstiles – Blocks set on an axis that turn 90 degrees when pushed by a character. They come in single, double, triple, and quadruple variations. They cannot turn if something is blocking their radius of movement. Blocks – Basic blocks of various sizes. They can be pushed by characters and may block paths necessary for a character to reach the stairs. Blocks can also fill holes to allow characters to walk past. Holes – Can't be walked over. Instead, blocks can be used to fill holes or characters must maneuver around the holes. At certain points in the game "Going Up?," one or all of Kwirk’s Veggie Friends will appear to help. They don’t have special abilities, but instead play exactly like Kwirk to allow maneuvers that weren't possible with only one character. The player switches between characters by pressing the select button and all of the four Veggie Friends must be brought to the stairs to clear the floor. The four Veggie Friends: Curly Carrot Eddie Eggplant Pete the Pepper Sass the Squash

Tomato Adventure (トマトアドベンチャー Tomato Adobenchā?) is a role-playing video game (RPG) developed by AlphaDream and published by Nintendo in Japan for the Game Boy Advance on January 25, 2002.

During battles against enemies, the player must fight using toy-like weapons called "Gimmicks",[2] which require the player to play a mini game correctly in order to land direct hits on the enemies, depending on which Gimmick the player uses. While using Gimmicks correctly, the player will earn stars for the extreme attacks, but if the player increases the difficulty of the Gimmicks, the player will increase the attack points of the Gimmicks and earn more stars, while the mini games would be more difficult than before. When one or two gears light up above the Gimmick meter, the player now has the choice to use one of two extreme attacks, if the player has a partner joined in. If the player fails in any mini game, the Gimmick meter will drop down to zero, and the player will have to start it all over. There are four different types of Gimmicks.

There are four types of Gimmicks:

Time - This type makes you finish a mini game that requires timing, like pressing a button whenever something comes to a certain part.

Speed - This type makes you finish a mini game that requires you to finish a task correctly before time runs out.

Excite (or Doki-Doki) - This type makes you finish miscellaneous mini games.

Input - This type makes you finish a mini game that either requires you to repeatedly hit the proper button(s) or to insert the information in a certain order or amount of times.

Star Fox is one of the most popular games of all time. The first Star Fox game had four levels in which there were four characters, Fox McCloud, Peppy Hare, Slippy Toad, and Falco Lombardi trying to save the galaxy. The first Star Fox (スターフォックス Sutā Fokkusu?), released as Starwing in Europe (to avoid confusion with an association named "StarVox" in Germany[1]), is the first game in the Star Fox series of video games, released on February 21, 1993 in Japan, on March 26, 1993 in North America, and on June 3, 1993 in Europe for the Super Famicom/Super Nintendo Entertainment System. It was the second three-dimensional Nintendo-developed game (behind 1992's X, also developed by Nintendo EAD together with Argonaut Software) but it is Nintendo's first game to use 3D polygon graphics. It accomplished this by being the first ever game to use the Super FX graphics acceleration coprocessor powered GSU-1. The complex display of three-dimensional models with polygons was still new and uncommon in console video games, and the game was much-hyped as a result. There are four players. In each level, Fox McCloud, is accompanied by three computer-controlled wingmen: Peppy Hare, Slippy Toad, and Falco Lombardi. Fox McCloud, the leader of the team, is accompanied by his teammates Falco Lombardi, Peppy Hare, and Slippy Toad- a sort of Fantastic Four elite fighting team

Star Fox Adventures was a later Star Fox game for Game Cube features both the established four main characters of the series—Fox, Falco Lombardi, Slippy Toad, and Peppy Hare, although Falco does not appear until near the game's end—and a host of new characters. Major additions are a quiet, mysterious blue fox named Krystal and the small dinosaur Prince Tricky, Fox's helper during the game. The entire planet is populated with dinosaurs, like the tyrannical General Scales, and other prehistoric animals such as pterosaurs and mammoths.[6] The entire game takes place on the world of Dinosaur Planet (in later games called "Sauria") and a number of detached pieces of the planet that are suspended in orbit around it. Dinosaur Planet is ruled by the EarthWalker tribe, which resemble Triceratops, and the rival CloudRunner tribe, similar to pterosaurs and birds. The SharpClaw tribe, which are the major antagonists in Adventures, are humanoid theropods.[6]

Super Smash brothers is a popular video game where four people can fight each other at one time. A common component of newer video games is they allow four people to play each other or with each other at one time

In Star Fox 64 Andross launches an attack across the Lylat system. The Star Fox team, now consisting of four members Fox, Peppy, Falco Lombardi and Slippy Toad have to defeat Andross. While traveling through several planets, including the Lylat system's star, Solar, and the asteroid field Meteo, the team battles with several of Andross' henchmen, including the rival mercenaries, Star Wolf. Star Fox was one of the most popular games in Nintendo 64.

In Star Fox 64 The Arwing is the primary craft used by the Star Fox team. The Arwing can use its boost meter to perform four special moves to avoid collisions and get the drop on pursuers: boost, brake, the U-turn, and the aforementioned somersault.

Fox 64 features multiplayer support for up to four players simultaneously.At first users can only play using the Arwing spaceship, but by earning certain medals in Story Mode, players can unlock the Landmaster tank, as well as the option to fight on foot as one of the four members of Star Fox equipped with a bazooka. Multiplayer is the only place where players can use a Landmaster with upgraded lasers.

Quadrature is a historical mathematical term that means calculating area. Quadrature problems have served as one of the main sources of mathematical analysis. Mathematicians of Ancient Greece, according to the Pythagorean doctrine, understood calculation of area as the process of constructing geometrically a square having the same area (squaring). That is why the process was named quadrature. For example, a quadrature of the circle, Lune of Hippocrates, The Quadrature of the Parabola. This construction must be performed only by means of compass and straightedge. Antique method to find the Geometric mean For a quadrature of a rectangle with the sides a and b it is necessary to construct a square with the side (the Geometric mean of a and b). For this purpose it is possible to use the following fact: if we draw the circle with the sum of a and b as the diameter, then the height BH (from a point of their connection to crossing with a circle) equals their geometric mean. The similar geometrical construction solves a problem of a quadrature for a parallelogram and a triangle. The area of a segment of a parabola Problems of quadrature for curvilinear figures are much more difficult. The quadrature of the circle with compass and straightedge had been proved in the 19th century to be impossible. Nevertheless, for some figures (for example Lune of Hippocrates) a quadrature can be performed. The quadratures of a sphere surface and a parabola segment done by Archimedes became the highest achievement of the antique analysis. The area of the surface of a sphere is equal to quadruple the area of a great circle of this sphere. The area of a segment of the parabola cut from it by a straight line is 4/3 the area of the triangle inscribed in this segment. For the proof of the results Archimedes used the Method of exhaustion of Eudoxus. In medieval Europe the quadrature meant calculation of area by any method. More often the Method of indivisibles was used; it was less rigorous, but more simple and powerful. With its help Galileo Galilei and Gilles de Roberval found the area of a cycloid arch, Grégoire de Saint-Vincent investigated the area under a hyperbola (Opus Geometricum, 1647), and Alphonse Antonio de Sarasa, de Saint-Vincent's pupil and commentator noted the relation of this area to logarithms. John Wallis algebrised this method: he wrote in his Arithmetica Infinitorum (1656) series that we now call the definite integral, and he calculated their values. Isaac Barrow and James Gregory made further progress: quadratures for some algebraic curves and spirals. Christiaan Huygens successfully performed a quadrature of some Solids of revolution. The quadrature of the hyperbola by Saint-Vincent and de Sarasa provided a new function, the natural logarithm, of critical importance. With the invention of integral calculus came a universal method for area calculation. In response, the term quadrature has become traditional, and instead the modern phrase "computation of a univariate definite integral" is more common.

The solution of the problem of squaring the circle by compass and straightedge demands construction of the number , and the impossibility of this undertaking follows from the fact that pi is a transcendental (non-algebraic and therefore non-constructible) number. If the problem of the quadrature of the circle is solved using only compass and straightedge, then an algebraic value of pi would be found, which is impossible. Johann Heinrich Lambert conjectured that pi was transcendental in 1768 in the same paper in which he proved its irrationality, even before the existence of transcendental numbers was proven. It was not until 1882 that Ferdinand von Lindemann proved its transcendence. The transcendence of pi implies the impossibility of exactly "circling" the square, as well as of squaring the circle. It is possible to construct a square with an area arbitrarily close to that of a given circle. If a rational number is used as an approximation of pi, then squaring the circle becomes possible, depending on the values chosen. However, this is only an approximation and does not meet the constraints of the ancient rules for solving the problem. Several mathematicians have demonstrated workable procedures based on a variety of approximations. Bending the rules by allowing an infinite number of compass-and-straightedge operations or by performing the operations on certain non-Euclidean spaces also makes squaring the circle possible. For example, although the circle cannot be squared in Euclidean space, it can be in Gauss–Bolyai–Lobachevsky space. Indeed, even the preceding phrase is overoptimistic.[7][8] There are no squares as such in the hyperbolic plane, although there are regular quadrilaterals, meaning quadrilaterals with all sides congruent and all angles congruent (but these angles are strictly smaller than right angles). There exist, in the hyperbolic plane, (countably) infinitely many pairs of constructible circles and constructible regular quadrilaterals of equal area. However, there is no method for starting with a regular quadrilateral and constructing the circle of equal area, and there is no method for starting with a circle and constructing a regular quadrilateral of equal area (even when the circle has small enough radius such that a regular quadrilateral of equal area exists).

In mathematics, quadrature is a historical term which means determining area. Quadrature problems served as one of the main sources of problems in the development of calculus, and introduce important topics in mathematical analysis.

Mathematicians of ancient Greece, according to the Pythagorean doctrine, understood determination of area of a figure as the process of geometrically constructing a square having the same area (squaring), thus the name quadrature for this process. The Greek geometers were not always successful (see quadrature of the circle), but they did carry out quadratures of some figures whose sides were not simply line segments, such as the lunes of Hippocrates and the quadrature of the parabola. By Greek tradition, these constructions had to be performed using only a compass and straightedge.

For a quadrature of a rectangle with the sides a and b it is necessary to construct a square with the side (the geometric mean of a and b). For this purpose it is possible to use the following: if one draws the circle with diameter made from joining line segments of lengths a and b, then the height (BH in the diagram) of the line segment drawn perpendicular to the diameter, from the point of their connection to the point where it crosses the circle, equals the geometric mean of a and b. A similar geometrical construction solves the problems of quadrature of a parallelogram and of a triangle.

The area of a segment of a parabola is 4/3 that of the area of a certain inscribed triangle.

Problems of quadrature for curvilinear figures are much more difficult. The quadrature of the circle with compass and straightedge was proved in the 19th century to be impossible. Nevertheless, for some figures (for example a lune of Hippocrates) a quadrature can be performed. The quadratures of the surface of a sphere and a parabola segment discovered by Archimedes became the highest achievement of analysis in antiquity.

The area of the surface of a sphere is equal to four times the area of the circle formed by a great circle of this sphere.

The area of a segment of a parabola determined by a straight line cutting it is 4/3 the area of a triangle inscribed in this segment.

For the proof of these results, Archimedes used the method of exhaustion[1]:113 of Eudoxus.

In medieval Europe, quadrature meant the calculation of area by any method. Most often the method of indivisibles was used; it was less rigorous than the geometric constructions of the Greeks, but it was simpler and more powerful. With its help, Galileo Galilei and Gilles de Roberval found the area of a cycloid arch, Grégoire de Saint-Vincent investigated the area under a hyperbola (Opus Geometricum, 1647),[1]:491 and Alphonse Antonio de Sarasa, de Saint-Vincent's pupil and commentator, noted the relation of this area to logarithms.[1]:492[2]

John Wallis algebrised this method; he wrote in his Arithmetica Infinitorum (1656) some series which are equivalent to what is now called the definite integral, and he calculated their values. Isaac Barrow and James Gregory made further progress: quadratures for some algebraic curves and spirals. Christiaan Huygens successfully performed a quadrature of the surface area of some solids of revolution.

The quadrature of the hyperbola by Saint-Vincent and de Sarasa provided a new function, the natural logarithm, of critical importance. With the invention of integral calculus came a universal method for area calculation. In response, the term quadrature has become traditional (some[who?] would say archaic), and instead the modern phrase finding the area is more commonly used for what is technically the computation of a univariate definite integral

In mathematics, a quadratrix (from the Latin word quadrator, squarer) is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and E. W. Tschirnhausen, which are both related to the circle.

The quadratrix of Dinostratus (also called the quadratrix of Hippias) was well known to the ancient Greek geometers, and is mentioned by Proclus, who ascribes the invention of the curve to a contemporary of Socrates, probably Hippias of Elis. Dinostratus, a Greek geometer and disciple of Plato, discussed the curve, and showed how it affected a mechanical solution of squaring the circle. Pappus, in his Collections, treats its history, and gives two methods by which it can be generated. Let a helix be drawn on a right circular cylinder; a screw surface is then obtained by drawing lines from every point of this spiral perpendicular to its axis. The orthogonal projection of a section of this surface by a plane containing one of the perpendiculars and inclined to the axis is the quadratrix. A right cylinder having for its base an Archimedean spiral is intersected by a right circular cone which has the generating line of the cylinder passing through the initial point of the spiral for its axis. From every point of the curve of intersection, perpendiculars are drawn to the axis. Any plane section of the screw (plectoidal of Pappus) surface so obtained is the quadratrix. Quadratrix of Dinostratus (in red) Another construction is as follows. DAB is a quadrant in which the line DA and the arc DB are divided into the same number of equal parts. Radii are drawn from the centre of the quadrant to the points of division of the arc, and these radii are intersected by the lines drawn parallel to AB and through the corresponding points on the radius DA. The locus of these intersections is the quadratrix. Quadratrix of Dinostratus with a central portion flanked by infinite branches Letting A be the origin of the Cartesian coordinate system, D be the point (a,0), a units from the origin along the x axis, and B be the point (0,a), a units from the origin along the y axis, the curve itself can be expressed by the equation[1] Because the cotangent function is invariant under negation of its argument, and has a simple pole at each multiple of π, the quadratrix has reflection symmetry across the y axis, and similarly has a pole for each value of x of the form x = 2na, for integer values of n, except at x = 0 where the pole in the cotangent is canceled by the factor of x in the formula for the quadratrix. These poles partition the curve into a central portion flanked by infinite branches. The point where the curve crosses the y axis has y = 2a/π; therefore, if it were possible to accurately construct the curve, one could construct a line segment whose length is a rational multiple of 1/π, leading to a solution of the classical problem of squaring the circle. Since this is impossible with compass and straightedge, the quadratrix in turn cannot be constructed with compass and straightedge. An accurate construction of the quadratrix would also allow the solution of two other classical problems known to be impossible with compass and straightedge, doubling the cube and trisecting an angle.

The quadratrix of Tschirnhausen[2] is constructed by dividing the arc and radius of a quadrant in the same number of equal parts as before. The mutual intersections of the lines drawn from the points of division of the arc parallel to DA, and the lines drawn parallel to AB through the points of division of DA, are points on the quadratrix. The cartesian equation is y=a cos 2a. The curve is periodic, and cuts the axis of x at the points x= (2n - I)a, n being an integer; the maximum values of y are =a. Its properties are similar to those of the quadratrix of Dinostratus.

The quadratrix was discovered by Hippias of Elis in 430 BC. It may have been used by him for trisecting an angle and squaring the circle. The curve may be used for dividing an angle into any number of equal parts. Later it was studied by Dinostratus in 350 BC who used the curve to square the circle. Hippias of Elis was a statesman and philosopher who travelled from place to place taking money for his services. Plato describes him as a vain man being both arrogant and boastful. He had a wide but superficial knowledge. His only contribution to mathematics seems to be the quadratrix.

The quadratrix or trisectrix of Hippias (also quadratrix of Dinostratos) is a curve, which is created by a uniform motion. It is one of the oldest examples for a kinematic curve, that is a curve created through motion. Its discovery is attributed to the Greek sophist Hippias of Elis, who used it around 420 BC in an attempt to solve the angle trisection problem (hence trisectrix). Later around 350 BC Dinostratus used it in an attempt to solve the problem of squaring the circle (hence quadratrix).

The quadratrix is mentioned in the works of Proklos (412–485), Pappos (3rd and 4th centuries) and Iamblichus (c. 240–325). Proklos names Hippias as the inventor of a curve called quadratrix and describes somewhere else how Hippias has applied the curve on the trisection problem. Pappos only mentions how a curve named quadratrix was used by Dinostratos, Nicomedes and others to square the circle. He neither mentions Hippias nor attributes the invention of the quadratrix to a particular person. Iamblichus just writes in a single line, that a curve called quadratrix was used bei Nicomedes to square the circle.[10][11][12] Though based on Proklos' name for the curve it is conceivable that Hippias himself used it for squaring the circle or some other curvilinear figure, most math historians assume that Hippias invented the curve but used it only for the trisection of angles. Its use for squaring the circle only occurred decades later and was due to mathematicians like Dinostratos and Nicomedes. This interpretation of the historical sources goes back to the German mathematician and historian Moritz Cantor.

Dinostratus (Greek: Δεινόστρατος, c. 390 BCE – c. 320 BCE) was a Greek mathematician and geometer, and the brother of Menaechmus. He is known for using the quadratrix to solve the problem of squaring the circle. Dinostratus' chief contribution to mathematics was his solution to the problem of squaring the circle. To solve this problem, Dinostratus made use of the trisectrix of Hippias, for which he proved a special property (Dinostratus' theorem) that allowed him the squaring of the circle. Due to his work the trisectrix later became known as the quadratrix of Dinostratus as well.[1] Although Dinostratus solved the problem of squaring the circle, he did not do so using ruler and compass alone, and so it was clear to the Greeks that his solution violated the foundational principles of their mathematics.[1] Over two thousand years later it would be proved impossible to square a circle using straight edge and compass alone.

Vector monitors were also used by some late-1970s to mid-1980s arcade games such as Star Wars and Asteroids.[1] Atari used the term Quadrascan to describe the technology when used in their video game arcades. The QUADRASCAN converter modulates the elevation and azimuth error signals in phase quadrature and adds them to the sum channel.

In electrical engineering, a sinusoid with angle modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are offset in phase by one-quarter cycle (π/2 radians). All three functions have the same frequency. The amplitude modulated sinusoids are known as in-phase and quadrature components.[1] Some authors find it more convenient to refer to only the amplitude modulation (baseband) itself by those terms. when φ happens to be such that the in-phase component is zero, the current and voltage sinusoids are said to be in quadrature, which means they are orthogonal to each other. In that case, no electrical power is consumed. Rather it is temporarily stored by the device and given back, once every seconds. Note that the term in quadrature only implies that two sinusoids are orthogonal, not that they are components of another sinusoid.

Quadrature amplitude modulation (QAM) is both an analog and a digital modulation scheme. It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves, usually sinusoids, are out of phase with each other by 90° and are thus called quadrature carriers or quadrature components — hence the name of the scheme.

In signal processing, a quadrature filter is the analytic representation of the impulse response of a real-valued filter: If the quadrature filter is applied to a signal , the result is which implies that is the analytic representation of . Since is an analytic signal, it is either zero or complex-valued. In practice, therefore, is often implemented as two real-valued filters, which correspond to the real and imaginary parts of the filter, respectively. An ideal quadrature filter cannot have a finite support, but by choosing the function carefully, it is possible to design quadrature filters which are localized such that they can be approximated reasonably well by means of functions of finite support.

In PSK, the constellation points chosen are usually positioned with uniform angular spacing around a circle. This gives maximum phase-separation between adjacent points and thus the best immunity to corruption. They are positioned on a circle so that they can all be transmitted with the same energy. In this way, the moduli of the complex numbers they represent will be the same and thus so will the amplitudes needed for the cosine and sine waves. Two common examples are "binary phase-shift keying" (BPSK) which uses two phases, and "quadrature phase-shift keying" (QPSK) which uses four phases, although any number of phases may be used. Since the data to be conveyed are usually binary, the PSK scheme is usually designed with the number of constellation points being a power of 2.

Constellation diagram for QPSK with Gray coding. Each adjacent symbol only differs by one bit. Sometimes this is known as quadriphase PSK, 4-PSK, or 4-QAM. (Although the root concepts of QPSK and 4-QAM are different, the resulting modulated radio waves are exactly the same.) QPSK uses four points on the constellation diagram, equispaced around a circle. With four phases, QPSK can encode two bits per symbol, shown in the diagram with Gray coding to minimize the bit error rate (BER) — sometimes misperceived as twice the BER of BPSK. The mathematical analysis shows that QPSK can be used either to double the data rate compared with a BPSK system while maintaining the same bandwidth of the signal, or to maintain the data-rate of BPSK but halving the bandwidth needed. In this latter case, the BER of QPSK is exactly the same as the BER of BPSK - and deciding differently is a common confusion when considering or describing QPSK. The transmitted carrier can undergo numbers of phase changes. Given that radio communication channels are allocated by agencies such as the Federal Communication Commission giving a prescribed (maximum) bandwidth, the advantage of QPSK over BPSK becomes evident: QPSK transmits twice the data rate in a given bandwidth compared to BPSK - at the same BER. The engineering penalty that is paid is that QPSK transmitters and receivers are more complicated than the ones for BPSK. However, with modern electronics technology, the penalty in cost is very moderate. As with BPSK, there are phase ambiguity problems at the receiving end, and differentially encoded QPSK is often used in practice. The implementation of QPSK is more general than that of BPSK and also indicates the implementation of higher-order PSK. Writing the symbols in the constellation diagram in terms of the sine and cosine waves used to transmit them: This yields the four phases π/4, 3π/4, 5π/4 and 7π/4 as needed. This results in a two-dimensional signal space with unit basis functions The first basis function is used as the in-phase component of the signal and the second as the quadrature component of the signal. Hence, the signal constellation consists of the signal-space 4 points The factors of 1/2 indicate that the total power is split equally between the two carriers. Comparing these basis functions with that for BPSK shows clearly how QPSK can be viewed as two independent BPSK signals. Note that the signal-space points for BPSK do not need to split the symbol (bit) energy over the two carriers in the scheme shown in the BPSK constellation diagram. QPSK systems can be implemented in a number of ways. An illustration of the major components of the transmitter and receiver structure are shown below. Although QPSK can be viewed as a quaternary modulation, it is easier to see it as two independently modulated quadrature carriers. With this interpretation, the even (or odd) bits are used to modulate the in-phase component of the carrier, while the odd (or even) bits are used to modulate the quadrature-phase component of the carrier. BPSK is used on both carriers and they can be independently demodulated. As a result, the probability of bit-error for QPSK is the same as for BPSK: However, in order to achieve the same bit-error probability as BPSK, QPSK uses twice the power (since two bits are transmitted simultaneously). The symbol error rate is given by: . If the signal-to-noise ratio is high (as is necessary for practical QPSK systems) the probability of symbol error may be approximated: The modulated signal is shown below for a short segment of a random binary data-stream. The two carrier waves are a cosine wave and a sine wave, as indicated by the signal-space analysis above. Here, the odd-numbered bits have been assigned to the in-phase component and the even-numbered bits to the quadrature component (taking the first bit as number 1). The total signal — the sum of the two components — is shown at the bottom. Jumps in phase can be seen as the PSK changes the phase on each component at the start of each bit-period. The topmost waveform alone matches the description given for BPSK above. Timing diagram for QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown at the top, and the total combined signal at the bottom. Note the abrupt changes in phase at some of the bit-period boundaries. The binary data that is conveyed by this waveform is: 1 1 0 0 0 1 1 0. The odd bits, highlighted here, contribute to the in-phase component: 1 1 0 0 0 1 1 0 The even bits, highlighted here, contribute to the quadrature-phase component: 1 1 0 0 0 1 1 0 Offset QPSK (OQPSK)[edit] Signal doesn't cross zero, because only one bit of the symbol is changed at a time Offset quadrature phase-shift keying (OQPSK) is a variant of phase-shift keying modulation using 4 different values of the phase to transmit. It is sometimes called Staggered quadrature phase-shift keying (SQPSK). Difference of the phase between QPSK and OQPSK Taking four values of the phase (two bits) at a time to construct a QPSK symbol can allow the phase of the signal to jump by as much as 180° at a time. When the signal is low-pass filtered (as is typical in a transmitter), these phase-shifts result in large amplitude fluctuations, an undesirable quality in communication systems. By offsetting the timing of the odd and even bits by one bit-period, or half a symbol-period, the in-phase and quadrature components will never change at the same time. In the constellation diagram shown on the right, it can be seen that this will limit the phase-shift to no more than 90° at a time. This yields much lower amplitude fluctuations than non-offset QPSK and is sometimes preferred in practice. The picture on the right shows the difference in the behavior of the phase between ordinary QPSK and OQPSK. It can be seen that in the first plot the phase can change by 180° at once, while in OQPSK the changes are never greater than 90°. The modulated signal is shown below for a short segment of a random binary data-stream. Note the half symbol-period offset between the two component waves. The sudden phase-shifts occur about twice as often as for QPSK (since the signals no longer change together), but they are less severe. In other words, the magnitude of jumps is smaller in OQPSK when compared to QPSK. π /4–QPSK[edit] Dual constellation diagram for π/4-QPSK. This shows the two separate constellations with identical Gray coding but rotated by 45° with respect to each other. This variant of QPSK uses two identical constellations which are rotated by 45° ( radians, hence the name) with respect to one another. Usually, either the even or odd symbols are used to select points from one of the constellations and the other symbols select points from the other constellation. This also reduces the phase-shifts from a maximum of 180°, but only to a maximum of 135° and so the amplitude fluctuations of –QPSK are between OQPSK and non-offset QPSK. One property this modulation scheme possesses is that if the modulated signal is represented in the complex domain, it does not have any paths through the origin. In other words, the signal does not pass through the origin. This lowers the dynamical range of fluctuations in the signal which is desirable when engineering communications signals. On the other hand, –QPSK lends itself to easy demodulation and has been adopted for use in, for example, TDMA cellular telephone systems. The modulated signal is shown below for a short segment of a random binary data-stream. The construction is the same as above for ordinary QPSK. Successive symbols are taken from the two constellations shown in the diagram. Thus, the first symbol (1 1) is taken from the 'blue' constellation and the second symbol (0 0) is taken from the 'green' constellation. Note that magnitudes of the two component waves change as they switch between constellations, but the total signal's magnitude remains constant (constant envelope). The phase-shifts are between those of the two previous timing-diagrams. SOQPSK[edit] The license-free shaped-offset QPSK (SOQPSK) is interoperable with Feher-patented QPSK (FQPSK), in the sense that an integrate-and-dump offset QPSK detector produces the same output no matter which kind of transmitter is used.[9] These modulations carefully shape the I and Q waveforms such that they change very smoothly, and the signal stays constant-amplitude even during signal transitions. (Rather than traveling instantly from one symbol to another, or even linearly, it travels smoothly around the constant-amplitude circle from one symbol to the next.) The standard description of SOQPSK-TG involves ternary symbols. DPQPSK[edit] Dual-polarization quadrature phase shift keying (DPQPSK) or dual-polarization QPSK - involves the polarization multiplexing of two different QPSK signals, thus improving the spectral efficiency by a factor of 2. This is a cost-effective alternative, to utilizing 16-PSK instead of QPSK to double the spectral efficiency. Any number of phases may be used to construct a PSK constellation but 8-PSK is usually the highest order PSK constellation deployed. With more than 8 phases, the error-rate becomes too high and there are better, though more complex, modulations available such as quadrature amplitude modulation (QAM). Although any number of phases may be used, the fact that the constellation must usually deal with binary data means that the number of symbols is usually a power of 2 to allow an integer number of bits per symbol