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Sharingan- (Literally means "Copy Wheel Eye" )The Sharingan is thought to be descended from the Byakugan, but grants the user different abilities and a different insight. The Sharingan does not automatically appear from birth in a user; instead, it will usually appear when the user is in a life-threatening situation, where the power of the Sharingan could save them. After this first appearance, the user can then call up the Sharingan any time they wish. The power of the Sharingan is judged through the number of tomoe in the eye, with a maximum of three in each.
The Sharingan's first and most well-known ability is to memorize any technique that it witnesses. It can memorize any standard form of jutsu with perfect accuracy, allowing the user to use the techniques as his own. In order to reproduce copied jutsu, however, one must have the necessary skill or ability to perform them.
The Sharingan's second ability is granting the user incredible clarity of perception, allowing them to track fast-moving objects with ease and even predict the subsequent movements of those objects. A fully-evolved Sharingan can track even the quickest opponents. This perception is also great enough to see through genjutsu and to observe the movement and flow of chakra, but not to the same extent or clarity as the Byakugan.
The Sharingan's third capability is a unique brand of hypnosis that involves suggesting actions and thoughts to the opponent. When used in conjunction with the aforementioned aspects of the Sharingan, this allows the user to perfectly mimic every move their opponent makes, even before they do, making it appear as if the user can see the future. It also allows for other forms of hypnotism, such as putting an opponent to sleep, replaying memories to someone else, creating various illusions to fool an opponent, or even controlling them.
Mangekyou Sharingan- (Literally means "Kaleidoscope Copy Wheel Eye" )Unlike the standard Sharingan, the Mangekyo Sharingan differs between users, changing the form of the Sharingan's tomoe seal when activated. Those who possess a Mangekyo Sharingan suffer from ever-deteriorating eyesight, a process that becomes faster through repeated usage and culminates in blindness. Only by taking the eyes of a sibling can one's eyesight be permanently restored, combining the appearances of the two Mangekyo Sharingan and granting them immense strength in the process.
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(Fully Developed)

(Itachi Mangekyou)

(Kakashi Mangekyou)

(Madara Mangekyou)

Ren'ngan- (Literally means "Samsara Eye" )Belongs to the leader of the Akatsuki, Pain. The possessor has the ability to use any jutsu other than bloodline limit jutsus such as Amaterasu or Tsukuyomi. The user can see through the eyes of clones or other bodies(such as Pain does), creating the ultimate 360 degree vision and defense.
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(Sorry if you needed more on the Ren'ngan, I had to go off of what I've read in the Manga.)
