Formation of a cusp of a branch   curve (animation)

The two pictures below illustrate projecting the (affine cubic) surface

     z^3 + x z + y = 0

to the (x,y) - plane. The branch curve in the (x,y) - plane, Delta = 27 y^2 + 16 x^3, which is a discriminant of this polynomial,

has an A_2 singularity. (In general, discriminant of an "universal polynomial" of degree d has singularity A_d-1)

(Both animations are made with the Surf program)

( For the Surf source code, see GitHub)

Semi-transparent version:

Non-transparent version: