This is a built-in and faster version of the Julia formula. 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 Switch feature to select good values.
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 normal formula that is less efficient, but offers more options. See Julia.