In recent years, fractal is widely used everywhere and escape time algorithm (ETA) became the most useful fractal creating method. However, ETA performs not so well because it needs huge computations. So, in this paper, we first present an improved fractal creating algorithm by symmetrical radius of k-M set. Meanwhile, we use distributed cooperative method to improve classic ETA into parallel system, which is called distributed cooperative ETA (DCETA). Secondly, we present the proof of fractal property in k-M set fcz=zk+c with exponent k (k
