The Swallowtail Singularity
The Swallowtail Singularity
This Demonstration shows one of the most frequently occurring objects in singularity theory: the swallowtail singularity. It is realized here as the subspace of consisting of all points such that +a+bx+c has multiple real roots. In addition, a section of the singularity surface by a plane is shown as a blue line. Such a section is a plane curve. As the level varies, the curve undergoes a metamorphosis (or a perestroika), which is exactly the same as that of a wave front on a plane.
3
{a,b,c}
4
x
2
x
a=t
t