The Mandelbrot set is 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. It is available as a fractal formula in Standard.ufm and as a fractal formula plug-in in Standard.ulb.

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. |

Power |
Specifies the exponent. The default value is (2, 0), resulting in the classic equation. Try (3, 0) and (4, 0) and so on to increase the number of main "buds". Non-integer values for the real part of the exponent will interpolate between these well-formed sets. If the imaginary part is not zero, the fractal will be further distorted. |

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**

- The Mandelbrot set is also available as a more efficient built-in formula with fewer options. See Mandelbrot (Built-in).
- The Mandelbrot set also acts as a map of Julia sets. Use Switch mode to switch to related Julia sets.

**See Also**

The Mandelbrot set

Standard formulas