Quantitative risk analysis is a method to evaluate risk and to identify areas for risk reduction. The final goal of our study is to propose an effective method for risk assessment of explosion hazard. To achieve the goal, a phenomenon that influences the consequences of explosion is first identified: self-turbulization and resulting acceleration of expanding flame during explosion. The fractal dimension is then identified as the key parameter that characterizes the phenomenon. Since the previous method to determine fractal dimension relies on large-scale explosion experiment, it has not been easy to determine fractal dimension. This paper demonstrates the possibility of determining fractal dimension by analyzing flame images of small-scale experiment, which might significantly reduce the cost of risk assessment of explosion hazard.