A ladder network constructed by an elementary two-terminal network consisting of a parallel resistor-inductor block in series with a parallel resistor-capacitor block sometimes is said to have a non-dispersive dissipative response. This special ladder network is created iteratively by replacing the elementary two-terminal network in place of the resistors. In this paper, it will be demonstrated that, in fact, non-dispersive dissipative response conclusion of this special ladder network is not accurate for steady-state condition. Furthermore, the voltage profile of this special ladder network exhibits a fractal form called the Levy C curve or Levy dragon in a certain condition. Therefore, this special ladder network may be called the Levy ladder network. This ladder network might be interesting for physics and electrical engineering students and they may encounter when dealing with this network series and parallel combinations of impedances. (Contains 6 figures.)