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The Swallowtail Singularity

​
level
-1
This Demonstration shows one of the most frequently occurring objects in singularity theory: the swallowtail singularity. It is realized here as the subspace of
3
consisting of all points
{a,b,c}
such that
4
x
+a
2
x
+bx+c
has multiple real roots. In addition, a section of the singularity surface by a plane
a=t
is shown as a blue line. Such a section is a plane curve. As the level
t
varies, the curve undergoes a metamorphosis (or a perestroika), which is exactly the same as that of a wave front on a plane.
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