Planar electrodes are increasingly used in a variety of neural stimulation techniques such as epidural spinal cord stimulation, epidural cortical stimulation, transcranial direct current stimulation and functional electric stimulation. Recently, optimized electrode geometries have been shown to increase the efficiency of neural stimulation by maximizing the variation of current density on the electrode surface. In the present work, a new family of modified fractal electrode geometries is developed to increase the neural activation function and enhance the efficiency of neural stimulation. It is hypothesized that the key factor in increasing the activation function in the tissue adjacent to the electrode is to increase the 'edginess' of the electrode surface, a concept that is explained and quantified by fractal mathematics. Rigorous finite element simulations were performed to compute the distribution of electric potential produced by proposed geometries, demonstrating that the neural activation function was significantly enhanced in the tissue. The activation of 800 model axons positioned around the electrodes was also quantified, showing that modified fractal geometries yielded a 22% reduction in input power consumption while maintaining the same level of neural activation. The results demonstrate the feasibility of increasing stimulation efficiency using modified fractal geometries beyond the levels already reported in the literature.