Mandelbrot

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.

The formula provides the following parameters:

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 

Starting point

well formed as the standard set. Try (0,  0.6), for example.

Specifies the exponent. The default value is (2, 0), resulting in the classic 

equation. 

z = z

2

 + c

Power

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.

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. 

Bailout value

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

G     

The Mandelbrot set is also available as a more efficient built in formula with fewer options. 

See 

Mandelbrot (Built in)

.

G     

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

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