The Julia set is closely related to the Mandelbrot set. For each complex number , the Julia set is the set of complex numbers whose orbit under iteration of is bounded. The Julia set fixes and allows the initial point , whose orbit gets computed, to vary. The set comprises those values whose orbits are bounded.

Use the cr and ci sliders to set the real and imaginary parts of the constant , then press Go to view . The program otherwise is controlled the same as the previous Mandelbrot program.

Julia sets

Here are the locations of some interesting Julia sets:¹

Use the text fields for cr and ci to input these values. Increase levels for maximum detail.