This package enables users of Julia lang to easily generate, explore, and share fractals of Julia, Mandelbrot, and Newton type. The name `Fatou`

comes from the mathematician after whom the Fatou sets are named.

**Definition** *(Julia set)*: For any holomorphic function on a complex plane, the boundary of the set of points whose result diverges when the function is iteratively evaluated at each point.

**Definition** *(Fatou set)*: The Julia set’s complement is the set of fixed limit points from holomorphic recursion.

**Definition** *(Mandelbrot set)*: The set of points on a complex parameter space for which the holomorphic recursion does not go to infinity from a common starting poin z_0.

**Definition** *(Newton fractal)*: The Julia/Fatou set obtained from the recursion of the Newton method z \mapsto z - m\cdot f(z) / f'(z) applied to a holomorphic function.

This package is supported on versions 0.5 to 0.7, and the newest release for 0.6 and 0.7 now relies on Reduce for symbolic computations with the Newton scheme.

See the wiki for many more detailed examples. Here is one of my own discovered examples

```
plot(mandelbrot(:(e^(-z)+cos(c)+im*sin(c*z)),∂=[-π,π,-2,2],n=700,N=80,cmap="jet",iter=false,p=-0.3) |> fatou, bare=true)
```

This is my favorite fractal made with the `Fatou`

package so far, I was completely surprised by what kind of crazy images you can make with this, using the function e^{-z} + \cos(c) + \sqrt{-1}\cdot\sin(c\cdot z) .

Also, if somebody has a good suggestion about how to make this package independent of PyPlot, while still retaining the same color maps that are available from PyPlot, then I am open to ideas and suggestions.

*It would be awesome if other Julians could post some of their own discoveries made with this package.*