A novel family of fractal curves is proposed which provides the designer a systematic way of miniaturizing the microwave components with the freedom of choosing among form factor, design complexity and achieved miniaturization. The proposed fractal curve is characterized by two integer values m and n. The m value determines the form factor of the fractal while n value governs the iteration number. The equations governing the geometry of fractals are also presented. The proposed fractal is characterized for miniaturization by designing a printed monopole antenna for various values of m and n. The results from the full wave simulations and experiments are analysed and explained. The effect of fractal on reducing the resonant frequency is quantified by an equation based on its physical interpretation. Based on this analysis, saturation point for miniaturization is established. The curves being symmetric around a straight line, distortionless radiation patterns are seen.