Since fractal is widely used in all science domains today, escape time algorithm, which is the most effective algorithm in drawing fractal figures, shows negatively when generation function is complex. In this paper, we improve classic escape time algorithm into cloud environment to improve its performance. At first, we provide a separation method of escape algorithm in cloud environment. Then we calculate complexity of the novel algorithm with a probability model based on allocation policy. At last, we use generalized fractal sets as experimental subjects to validate our conclusion. Experimental results show correctness and rapidness of the novel algorithm.