  The large class of moving boundary processes in the plane modeled by the
so-called Laplacian growth, which describes, e.g., solidification,
electrodeposition, viscous fingering, bacterial growth, etc., is known to be
integrable and to exhibit a large number of exact solutions. In this work, the
boundaries are assumed to be in the class of lemniscates with all zeros inside
the bounded component of the complex plane. We prove that for any initial
boundary taken from this class, the evolving boundary instantly stops being in
the class, or else Laplacian growth destroys lemniscates instantly.
