Zeros (black disks) and critical points (blue squares) of a random degree 50 polynomial tend to appear in pairs. The colored lines are the gradient flow lines for the modulus squared of the random pol

The purple (resp. white) regions are where are random eigenfunction of the isotropic harmonic oscillator is negative (resp. postive). The interface between these purple and white regions is therefore

The colored lines are the gradient flow lines for the modulus squared of the random polynomial, which is almost surely a Morse function.