The fractal dimension property of 40Hz event related potentials(ERPS) is studied for tests of Chinese word short term memory recognition, mental arithmetic calculation and short term memory capacity. By comparison it is found that there is a remarkable difference in the fractal dimensions of 40Hz ERPS for different cognitive tasks. Meanwhile, for the identical cognitive process, there is a distinct hemispheric difference in fractal dimension property of 40Hz ERPS, which indicates that there exists a noticeable difference in the property of brain dynamical between the two hemispheres under different cognitive tasks. The fractal dimension property of 40Hz event related potentials (ERPS) is studied for tests of Chinese word short term memory recognition, mental arithmetic calculation and short term memory capacity. By comparison it is found that there is a remarkable difference in the fractal dimensions of 40Hz ERPS for different cognitive tasks. Meanwhile, for the identical cognitive process, there is a distinct hemispheric difference in fractal dimension of 40 Hz ERPS, which indicates that there exists a noticeable difference in the property of brain dynamical between the two hemispheres under different cognitive tasks .