  Eigenspectra that fill regions in the complex plane have been intriguing to
many, inspiring research from random matrix theory to esoteric semi-infinite
bounded non-Hermitian lattices. In this work, we propose a simple and robust
ansatz for constructing models whose eigenspectra fill up generic prescribed
regions. Our approach utilizes specially designed non-Hermitian random
couplings that allow the co-existence of eigenstates with a continuum of
localization lengths, mathematically emulating the effects of semi-infinite
boundaries. While some of these couplings are necessarily long-ranged, they are
still far more local than what is possible with known random matrix ensembles.
Our ansatz can be feasibly implemented in physical platforms such as classical
and quantum circuits, and harbors very high tolerance to imperfections due to
its stochastic nature.
