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.

Julia is available as a fractal formula in Standard.ufm and as a fractal formula plug-in in Standard.ulb.

The following parameters are provided:

Julia seed

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 Switch feature to select good values.

Power

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

z = z² + c

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.

Bailout value

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.

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).