  We consider perturbations of the complex quadratic map $ z \to z^2 +c$ and
corresponding changes in their quasi-Mandelbrot sets. Depending on particular
perturbation, visual forms of quasi-Mandelbrot set changes either sharply (when
the perturbation reaches some critical value) or continuously. In the latter
case we have a smooth transition from the classical form of the set to some
forms, constructed from mostly linear structures, as it is typical for
two-dimensional real number dynamics. Two examples of continuous evolution of
the quasi-Mandelbrot set are described.
