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A fractal was a repeating geometric pattern with no end. This pattern could occur in nature or in mathematics, where it was the same at all levels of scale.

As part of a diagnostics program run on The Doctor in 2373, he was asked to focus on an animation of fractal patterns. (VOY: "The Swarm")

In 2376, on the Qomar homeworld, Tincoo was inspired by The Doctor into creating a musical composition based on two fractals. (VOY: "Virtuoso")

The script of Star Trek contained some additional questions and answers that could be used in the skill dome scene, including a question which asked to calculate the dimensionality of a certain fractal.

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