Julia

Julia sets are closely related to the well known 

Mandelbrot set

. In fact, 

the Mandelbrot set is a map of Julia sets. For each point in the 

Mandelbrot set, there exists a unique Julia set.

Use the 

Switch feature

 to select a Julia set by moving the mouse cursor 

over a Mandelbrot fractal. The most interesting Julia sets are found at 

points close to the edge, where the colors change quickly.

Julia sets are strictly 

self similar

 and less complex than the Mandelbrot set. Still, they can be 

strikingly beautiful, and they are certainly very interesting to explore.

The formula provides the following parameters:

This parameter specifies the point in the Mandelbrot set that corresponds to 

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

Julia seed

Switch feature

 to select good values.

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 symmetry order. Non integer 

values for the real part of the exponent or non zero values for the imaginary 

part will distort the fractal.

Specifies the magnitude of z that will cause the formula to stop iterating. To 

obtain "true" Julia sets, this should be set to 4 or larger. Larger values tend to 

smooth the outside areas. 

Bailout value

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

Note: The Julia formula is also available as a more efficient built in formula with fewer options. See 

Julia (Built in)

.

See Also

Lambda (Julia, Mandelbrot)

Julia sets

Standard formulas

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