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Sigmafor other, similarly-named pages.
In 4126, the Ood brain managed to reconnect to Ood Sigma despite his link having been severed through the translator orb. Sigma was made a focus of the Brain's intelligence and mercy, and also its representative, in a sense. This allowed him to function as an individual and drug Halpen's hair tonic with Ood graft to transform him in to an Ood. For some time, Sigma had remained by Halpen's side while other Ood succumbed to red-eye. As Sigma was already reconnected to the Ood Brain, he was immune to the rage and anger which subsequently infected the other Ood. He led the Tenth Doctor and Donna Noble to the room containing the Ood Brain.
There Sigma revealed to Halpen he had been dosing him with a liquid, disguised as hair tonic, which turned Halpen into an Ood. While the red eye-infected Ood had been "contaminated" by the Ood Brain's anger, Sigma had become the focus of the brain's patience as he transformed Halpen. Sigma declared that the Ood would look after Halpen.
As the Doctor and Donna departed, Sigma assured them that they would always be remembered as friends of Ood-kind, and would have a part in the song for as long as the Ood existed. However, he ominously remarked the Doctor's song would soon come to an end. (TV: Planet of the Ood)
The vision was actually Sigma trying to summon the Doctor to the 43rd century, as the Ood were experiencing visions of the Master. When the Doctor responded to his message, Sigma seemed disturbed that the Doctor had taken so long. He told the Doctor that it took them 100 years to make Ood Sphere better. The Doctor was amazed and somewhat worried at the progress they had made in 100 years. Sigma took him to the Ood Elder to try to warn him of the impending danger. When the Ood held hands, Sigma did not. When the Elder foretold the "end of time", the Doctor left abruptly.
After the events that led to the Doctor and the Master saving the universe from Rassilon and the other returning Time Lords, the Doctor bade farewell to all of his companions. In 2005, after briefly talking to a younger Rose Tyler, the Doctor began to experience increased effects of his impending regeneration. Just before the Doctor returned to the TARDIS, Ood Sigma appeared to him again. He told him that the universe would sing him to his rest, and that while this song was ending, his story would never end. The Ood all joined together in song as the Doctor stumbled into the TARDIS to regenerate into his eleventh incarnation. (TV: The End of Time)
Ood Sigma was a very patient Ood, and, as he was the first Ood to reconnect with the Ood brain, he was the only known Ood who was immune to the fits of rage that infected other members of his species. Klineman Halpen mistakenly thought this was because of loyalty. He was able to act independently instead of doing what every other Ood did. A cunning creature, Sigma acted like a loyal servant whilst secretly giving Halpen a liquid that would turn him into an Ood. He grew to think of the Doctor and Donna as his friends and stood between them and his former master when Halpen aimed a gun at them. Despite his dislike of Halpen, Sigma said he would look after him after turning him into an Ood. (TV: Planet of the Ood)
When the Doctor and Sigma were reunited, the Doctor told jokes in an attempt to liven things up. Sigma remained impassive and the Doctor grumbled about him possessing no sense of humour. However, Sigma later showed the Doctor further kindness by easing his transformation into his next incarnation. (TV: The End of Time)
Behind the scenes
According to The Brilliant Book 2012, Sigma was helping the Doctor in his attack on Demon's Run, explaining why Russell T Davies is given credit for creating the Ood in A Good Man Goes to War even though no Ood was seen.