# Fractals/Mathematics/rotating

< Fractals

Rotation map defines dynamical systems on the circle ( maps of the circle to itself = self-maps on the circle). The theory describing it is called **Rotation Theory**^{[1]}

"If a is rational, then every point is periodic. If a is irrational, then every point has a dense orbit." David Richeson^{[2]}

#### rational

editRotation map describes counterclockwise rotation of point thru turns on the unit circle:

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It is used for computing: