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Tomoe (巴, also written 鞆絵),[a] commonly translated as "comma", is a comma-like swirl symbol used in Japanese mon (roughly equivalent to a heraldic badge or charge in European heraldry). It closely resembles the usual form of a magatama.
The tomoe appears in many designs with various uses. The simplest, most common patterns of the device contain from one to four tomoe, and are reminiscent of similar designs that have been found in wide distribution around the world. When circumscribed in a circle, it often appears in a set of three, with this design known as the mitsudomoe (三ツ巴).
The mitsudomoe is also the logo of the OBS Studio application since it released in 2012.
The character 巴 (Chinese pronunciation bā) has several meanings, ranging from a Sichuan toponym to a crust formed by dryness, parts of the body such as hands or cheeks, and, as a verb, bearing the sense of "to hope", "expect" or "be anxious over". The Chinese character used to depict, according to Bernhard Karlgren's interpretation of the small seal script graph, a python. The Japanese word itself may be of Mongolic origin, since it bears comparison with Middle Mongolian tomuγa (twisted horse headdress, from the verb tomu (plait, twist)) and Ordos t'omok ('a little bag hung on a horse's head'). In this latter connection Tang ceramic figures of horses show small sacks tethered to the lower neck, perhaps to stop the horse from throwing its head back.
One view is that the word refers to a picture e (絵) of a tomo (鞆), or drawings on the latter, the tomo in question, in archaic Japanese tömö,[b] being a round leather arm protector, like the bracer or gauntlet tab of European archery. Roy Andrew Miller describes it as "a small hollow sack or bulb of sewn leather with leather tie straps, sometimes embossed with a comma like decorative device (tomoe) of continental origin". It was worn on the left elbow or wrist of an archer either to prevent chafing from the bowstring (tsuru: 弦) twanging back to position on the release of an arrow, or to strike fear into the enemy from the sharp sound caused by the bowstring hitting the wrist guard. The 'tomo picture' (tomoe) can therefore be interpreted either as a visual pun on the tomo represented, or, otherwise, as taking its name from that object. Several such examples are conserved in Nara at the Shōsōin. 
An alternative interpretation takes it to be a stylized magatama.
The origin of the tomoe design is uncertain. A pattern resembling the two-comma tomoe (futatsudomoe) has been found in ancient cultures on all inhabited continents.  A stylized design on a Yangshao bowl dates back to 2,000 BCE. The motif of two encircling dolphins biting each other's tails has been found on Cretan ceramics dating from the Minoan period (1700-1400 BCE), and the two fish biting each other in circular fashion recurs in both Chinese and Central Mexican ware. It is frequently seen on prehistoric Celtic remains, and one mirror from Balmaclellan is almost identical to the mitsudomoe.  In China, the double comma form came to be assimilated to the Yin-Yang philosophy of opposing male/female principles, formalized in the Tàijítú design of the late Song Dynasty period.[c] This in turn recurs in the 7th century in Korea, where it was known as Taegeuk. and replicated in the Japanese futatsudomoe and mitsudomoe patterns, the former in association with divinatory rites, the latter frequently linked to temple drums with apotropaic functions. According to Jean Herbert in these contexts, the mitsudomoe embodied three spirits, the yin-yang dyad being represented by an aramitama (rough kami) and a nigimitama (gentle kami), while the third comma denoted the sakimitama, or lucky spirit.[d]
N. Gordon Munro argued that the basis for the mitsudomoe pattern, a motif found also among the Ainu, was the eastern European and western Asian figure of the triskelion, which he believed lay behind the Chinese three-legged crow design, and, in his view, its reflex in the mythical Japanese crow, the Yatagarasu (八咫烏).
As a leather[e] wrist protector tomo appear to have been employed at least as early as the Kofun period, where they are frequently attested on haniwa terracotta figurines depicting archers,  and may even have had, aside from their military function, a ritual or fetish value, perhaps related to their phallic shape.
The tomoe emblem established itself as a common emblem during the Fujiwara ascendency of the late Heian period, around the 10th-11th centuries, and proliferated through to Kamakura times. It is thought that a resemblance between the tomoe and the Emperor Ōjin found in the Nihongi may also account for its rising popularity among samurai, since Ōjin was apotheosized as a god in Hachiman shrines.
In the Nihongi account, when Ōjin was born, inspection of his body revealed a fleshy growth on his arm similar to a warrior's wrist or elbow pad, and for this reason he was called homuta (誉田: lit.(Lord) Armguard) (OJ: pomuda),[f] an old word for a tomo.[g]
Fragmentary sources suggest that the First Shō dynasty, who founded the Ryukyu Kingdom, used the symbol if not as their family crest. American historian George H. Kerr claims that King Shō Toku adopted the mitsudomoe as the crest of the royal house after his successful invasion of Kikai Island in 1465.(Kerr 2011, p. 101) The Second Shō dynasty, who ruled the Ryukyu Kingdom from 1470 to 1879, adopted the mitsudomoe as its family crest. Since it was the royal family crest, its usage was once severely restricted. Okinawans who visited Japan shortly after the kingdom's annexation in 1879 were surprised that mitsudomoe banners were flown everywhere. During the American military occupation of Okinawa Prefecture, the United States Civil Administration of the Ryukyu Islands (USCAR) made a failed attempt to recreate a Ryukyuan national flag with a mitsudomoe, only to find that Okinawans were apathetic towards, or did not recognize, the former royal family's symbol. Today the symbol is still regarded as a symbol for Ryukyu and, to a lesser extent, Okinawa.
The mitsudomoe is closely associated with Shinto shrines, in particular those dedicated to Hachiman, the god of war and archery. Hachiman in Shinto cosmology and ritual, as for example at Hakozaki Shrine, is repeatedly connected with the number three. In Shintoist thinking, this number is taken to represent the three aspects of the four mitama or 'souls' (the other, the kushimitama being considered far rarer).
It is also commonly displayed on banners and lanterns used in festivals and rituals related to Amaterasu-ōmikami, who in the Kojiki confronts her brother Susanoo when he usurps her terrain on earth by dressing as an archer, adorned with magatama beads and 'an awesome high arm-guard' (itu nö takatömö).[h]
A third element of its symbolic panorama concerns water, an association engendered by its swirling pattern. For this reason, it is said to be located on roofs and gables as a charm against fire.
Since Hachiman was worshipped as the guardian of warriors, it was adopted as a common design element in Japanese family emblems (家紋, kamon) by various samurai clans such as the Nagao, Kobayakawa and Utsunomiya. Among aristocrats, the Saionji family used it as its family emblem. The Koyasan Shingon sect of Buddhism uses the mitsudomoe as a visual representation of the cycle of life.
Tomoe also is a personal name, dating at least back to Tomoe Gozen (巴御前), a famous female warrior celebrated in The Tale of the Heike account of the Genpei War. In Kyoto's Jidai Matsuri festival, she appears in the Heian period section of the procession in samurai costume, and parades as a symbol of feminine gallantry.
The tomoe has also been adopted as a corporate logo in Japan.
The two-fold tomoe is almost identical in its design elements to the Chinese symbol known as a taijitu, while the three-fold tomoe is very similar to the Korean tricolored taegeuk. Also note that the negative space in between the swirls of a fourfold tomoe forms a swastika-like shape, which is fairly prominent in many Indian religions such as Hinduism and Jainism and Buddhism. A similar design can also be found in the some forms of the Celtic spiral triskele as well as with the Basque lauburu and the Sicilian Trinacria.