The left yellow dot, marks the parameter belonging to the Mandelbrot set, which gives rise to the connected Julia set in figure 1. The right yellow dot marks the parameter outside the Mandelbrot set, which gives rise to the disconnected Julia set in figure 2. The Mandelbrot set on the other hand, resides in the parameter plane, i e the c-plane. The term cubics refers to 3-degree polynomials, i e the highest power of the variable z is three. The first funny thing are the critical points.
Cubic polynomials happen to have two of that kind.
Both critical points have orbits that tend to infinity. One critical point has an orbit that tends to infinity, and the other critical point has a bounded orbit. This is the new case compared with quadratic polynomials, which only has one critical point. The resulting Julia set is disconnected but only in rare cases the set is a totally disconnected Cantor set. In most cases the Julia set encloses domains where one of the critical points belongs to such a domain.