Julia sets often echo the shapes of the Mandelbrot set from which their control point is selected. This crop of a Julia set is uncannily similar to the Mandelbrot set from the region of its control point.
Click this link to see the Mandelbrot set centered on this Juila set's control point:
Julia-Mandelbrot pair Mandelbrot
Fractal type: Julia set
Plot size (w,h): 800, 600
Maximum iterations: 65000
Center Point (real, imaginary): -0.000265, -0.000265 i
Plot Width (real): 0.424
Julia origin (real, imaginary): -1.768408652832383, 0.002511307955152072 i
Fractalworks plot Julia-Mandelbrot pair Julia