Mandelbrot (Built-in)

This is a built-in and faster version of the standard Mandelbrot set: the most well-known fractal type. Although it is calculated by a simple formula, it is incredibly complex. As you zoom in, more and more ever-changing detail becomes visible, such as little "baby" Mandelbrot sets and all kinds of spirals.

Because the Mandelbrot set lends itself well to basic zooming and exploring, it is a good starting point if you are new to fractals.

The formula provides the following parameters:

Starting point

For the standard Mandelbrot set, this should be set to (0, 0). Other values create distorted shapes that can be interesting, but they are usually not as well-formed as the standard set. Try (0, -0.6), for example.

Bailout value

Specifies the magnitude of z that will cause the formula to stop iterating. To obtain the "true" Mandelbrot set, this should be set to 4 or larger. Larger values tend to smooth the outside areas.

With the Basic coloring algorithm and the Color Density set to 4, try the bail-out values 4 and then 16 to see the difference.

Some coloring algorithms require specific bail-out values for good results.

Notes

There is also a version of the Mandelbrot set as a normal formula (not built-in). Although it is less efficient, it offers more options, and it is better at handling very large bail-out values. See Mandelbrot.
The Mandelbrot set also acts as a map of Julia sets. Use Switch mode to switch to related Julia sets.