This disconnected Julia set is taken from the cleft in the cardioid of a "baby mandelbrot" which, in turn, is from a tendril on a "dragon" shape off the primary baby mandelbrot on the real axis.

The Julia set's "C" value is -1.768769335356247, 0.0021629355446189i.
It's a closeup of the center of the julia set, at a plot width of 0.00115644.

If you have installed FractalWorks 0.4.0 or later, click here to create this plot on your computer.

The colors may look slightly different, as they were adjusted for this plot.