Theoretically infinite repetition of a calculation process, the application of a function or a reasoning process.

### Example

- Fractal objects are the result of iterations of iterated functions.

This fractal geometric figure was generated using an iterated function system.

- Consider an initial positive real number
*x*; if the square root of the number is taken, then the square root of the result is taken, and this operation is repeated a large (theoretically infinite) number of times, we obtain 1 :

\(\sqrt{\sqrt{\sqrt{\sqrt{x}}}} … = 1\).