Good real perturbation of the map germ f_t(x,y)=(x,y^6+xy+ty^4-ty^2), (target singularities), and the discriminant curve has homotopy type of wedge of six circles.

Real deformation of r-stable singularities, r=0,1,2, in the source of the map germ from C3 to C3 given by f_t(x,y,z)=(x,y,z^6+yz+xz^2+tz^4). 

• 0-stable types:  A12-singularities (yellow color); A3-singularities (green color); A111-singularities (black color).

• 1-stable type: A2-singularities (blue color); A11-singularities (red color).

• 2-stable type: A1-singularities (gray color).

Running over the cuspidal edge in the source... 

Real deformation of r-stable singularities, r=0,1,2, in the target of the map germ from C3 to C3 given by f_t(x,y,z)=(x,y,z^6+yz+xz^2+tz^4). 

• 0-stable types:  A12-singularities (yellow color); A3-singularities (green color); A111-singularities (black color).

• 1-stable type: A2-singularities (blue color); A11-singularities (red color).

• 2-stable type: A1-singularities (gray color).