Lambda (Julia, Mandelbrot)

The Lambda formula is an alternative version of the equation for 

Julia

fractals. While it is capable of creating the same Julia sets, the 

corresponding Mandelbrot version looks different.

Because the Mandelbrot version is a map of Julia sets, this allows you to 

find Julia sets with the 

Switch feature

 in a different way than with the 

usual 

Mandelbrot

 set. It is easier to find good spirals and other 

interesting Julia sets.

The formulas provide the following parameters:

For the standard Lambda Mandelbrot set, this should be set to (0.5, 0). Other 

values create distorted shapes that can be interesting, but they are usually not 

as well formed as the standard set. 

Start Value

(Mandelbrot only)

For well formed sets, the real value should be set to 1 divided by the real 

value of the exponent. For example, use (0.25, 0) if Exponent is set to (4, 0).

This parameter specifies the point in the Mandelbrot version that corresponds 

Julia Seed

to the current Julia set. It defines the shape and behavior of the Julia set. Use 

(Julia only)

the 

Switch feature

 to select good values.

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

equation. 

c * z * (1   z)

Exponent

Try (3, 0) and (4, 0) and so on to increase the complexity of the fractal. 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 well formed fractals, this should be set to 4 or larger. Larger values 

tend to smooth the outside areas. 

Bailout

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

See Also

Julia sets

Standard formulas

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