The fractal dimension in the electrical corona discharge varying experimental setups and simulation methods was considered in this research. We can use the fractal dimension as a parameter that describe the growth phenomena systems like DLA or DBM. By the means of the fractal dimension, we can also classify the systems with a universality. Hence we have used capacity(box-counting dimension) as a tool to investigate the growth of streamers in the corona discharge. This work is made of summarizing of theories, computer simulations and comparing with analyzed experimental results. Before this work, there were several problems on describing the experimental setups which had mismatched the result of stochastic simulation method (D~1.7). Our experiment with the setup of needle-plate electrodes which had been reported in the previous work resulted in D~2.0 of a random growth condition. but the stochastic simulation gave the results of D~1.7. It became known by the new experiment that the setup of needle-ring electrodes could explain well the result of the stochastic model. In case of the setup of needle-plate electrodes, we assumed that the growth of corona streamer was under the influence of the film surface and have constructed a new simulation model(FSEAM) which gave the same fractal dimension with the experiment(D~2.0). We also got a graph of the η-D multifractal. This graph implies the dependence of a growth possibility on a local electric field. From this graph and the experimental result of the setup of needle-ring electrodes we have known that the streamer growth rate is proportional to the local electric field(η~1.0). With this result we also simulated about a 3D boundary condition. It has resulted in D~2.0.