## 12.4 The `fractals` module

**fractals.julia(,,)**

The fractals.julia(,,) function tests whether the point in the complex plane lies within the Julia set associated with the point in the complex plane. The expression is iterated until either , in which case the iteration is deemed to have diverged, or until iterations have been exceeded, in which case it is deemed to have remained bounded. The number of iterations required for divergence is returned, or is returned if the iteration remained bounded – i.e. the point lies within the numerical approximation to the Julia set.

**fractals.mandelbrot(,)**

The fractals.mandelbrot(,) function tests whether the point in the complex plane lies within the Mandelbrot set. The expression is iterated until either , in which case the iteration is deemed to have diverged, or until iterations have been exceeded, in which case it is deemed to have remained bounded. The number of iterations required for divergence is returned, or is returned if the iteration remained bounded – i.e. the point lies within the numerical approximation to the Mandelbrot set.