Two new types of irregular scaling equations—strange scaling equations are obtained by the continuous expansion method and scale expansion theory. This paper explores the differences and advantages of the rational function sequences of strange scaling equations in terms of computational effectiveness, computational performance, and operational oscillation period. It is proved by the zero pole distribution in the complex plane that the strange scale equations are physically achievable, and the approximation performance is summarized. These equations propose a new model and a new idea for the realization and design of the fractance approximation circuits. From the localized features of the zero pole and the frequency characteristics, the reason for the operational oscillation of any physically achievable irregular scaling equation is found.
