Distributed Cooperative Algorithm for k-M Set with Negative Integer k by Fractal Symmetrical Property

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 f(c) (z) = z(k) + c with exponent k (k < 0), which concludes its threshold and symmetrical property. Finally, computational result shows correctness of the novel DCETA, which shows better computational effectiveness and lower waste.