The animation in this page shows the changes in shape of the
basin of attraction for the dynamical system :

x = x*y+a*x-y
y = x+y

as the parameter a varies from 0.4 to 0.75.

The basin of attraction is the set of all initial points in phase space
that are drawn to the attractor. The basin boundaries are sometime smooth and
sometime they are fractals. By coloring the points just outside the basin
according to the number of iterations required for them to leave some region
surrounding the attractor (in this case a square) you can produce
the so called escape-time fractals.