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We investigate terahertz characteristics of split ring resonators (SRRs) with fractal structure. By applying the fractal structure of Koch curve to the SRRs, the electric and magnetic resonant frequencies can be modified. The position of the resonant frequencies shifts to lower frequency as the fractal level of Koch curve increases. This result shows the possibility of fabricating metamaterials with the extremely small unit cell as compared to the wavelength at operational frequency.