Distributional Escape Time Algorithm Based on Generalized Fractal Sets in Cloud Environment

LIU Miao; LIU Shuai; FU Weina; ZHOU Jiantao

Article Contents

Article Navigation > Chinese Journal of Electronics > 2015 > 24(1): 124-127

LIU Miao, LIU Shuai, FU Weina, et al., “Distributional Escape Time Algorithm Based on Generalized Fractal Sets in Cloud Environment,” Chinese Journal of Electronics, vol. 24, no. 1, pp. 124-127, 2015,

Citation:

LIU Miao, LIU Shuai, FU Weina, et al., “Distributional Escape Time Algorithm Based on Generalized Fractal Sets in Cloud Environment,” Chinese Journal of Electronics, vol. 24, no. 1, pp. 124-127, 2015,

Citation:

PDF( 319 KB)

Distributional Escape Time Algorithm Based on Generalized Fractal Sets in Cloud Environment

1.
College of Computer Science and Technology, Jilin University, Changchun 130012, China;
2.
College of Computer, Inner Mongolia University, Hohhot 010012, China;
3.
School of Physical Science and Technology, Inner Mongolia University, Hohhot 010012, China

Funds: This work is supported by grants Programs of Higher-level Talents of Inner Mongolia University (No.125126, No.115117), Project of Higher School in Inner Mongolia (No.NJZY13004), National Natural Science Foundation of Inner Mongolia (No.2014BS0606), Key Project of Chinese Ministry of Education (No.212025), Inner Mongolia Science Foundation for Distinguished Young Scholars (No.2012JQ03), Science and Technology Development Plan of Jilin Province (No.20130101047JC), National Natural Science Foundation of China (No.61261019, No.61262082, No.31160253, No.31360289, No.61300146).

More Information

Corresponding author: LIU Shuai born in 1982, Ph.D. and associate professor. His interesting area contains pattern recognition, chaotic system and applied mathematics. (Email: cs_liushuai@imu.edu.cn)
Received Date: 2013-05-01
Rev Recd Date: 2013-06-01
Publish Date: 2015-01-10

Abstract

Abstract

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.
- Escape time algorithm,
- Fractal,
- Distribution probability model,
- Cloud environment

FullText(HTML)

References(14)

References

BB. Mandelbrot, The Fractal Geometry of Nature, San Fransisco, Freeman W H, pp.1-122, 1982.

J. Falconer, Fractal Geometry: Mathematical Foundations and Applications, 2nd Edition, John Wiley. Sons Inc., New York, pp.1-250, 2003.

S. Liu, X. Che and Z. Wang, "Improvement of escape time algorithm by no-escape-point", Journal of Computers, Vol.6, No.8, pp.1648-1653, 2011.

J.P. Dumont and C.A. Reiter, "Visualizing generalized 3x+1 function dynamics", Computers and Graphics, Vol.25, No.5, pp.553-595, 2001.

S. Liu and Z.Wang, "Fixed point and fractal images for a generalized approximate 3x+1 function", Journal of Computer-Aided Design and Computer Graphics, Vol.21, No.12, pp.1740-1744, 2009. (in Chinese)

P. Mell and T. Grance, "The NIST definition of cloud computing", National Institute of Standards and Technology, Vol.53, No.6, pp.50, 2009.

M. Armbrust, et al., "A view of cloud computing", Communications of the ACM, Vol.53, No.4, pp.50-58, 2010.

R.N. Calheiros, R. Ranjan, A. Beloglazov et al, "CloudSim: A toolkit for modeling and simulation of cloud computing environments and evaluation of resource provisioning algorithms", Software: Practice and Experience, Vol.41, No.1, pp.23-50, 2011.

C. Lam, Hadoop in Action, Manning Publications Co., New York, 2010.

T. White, "Hadoop: The definitive guide: the definitive guide", USA, O’Reilly Media, Inc., 2009.

X.Y. Wang and X.J. Yu, "Study the dynamic theory of generalized 3x+1 function based on fractal visual method", Progress in Natural Science, Vol.17, No.4, pp.529-535, 2007. (in Chinese)

S. Liu, X. Che and Z.Wang, "Existence domain analysis and numerical algorithm of fixed point for generalized 3x+1 function T(x)", Acta Electronica Sinica, Vol.39, No.10, pp.2282-2287, 2011. (in Chinese)

S. Liu, W. Fu, H. Deng, et al., "Distributional escape time algorithm with fractal images in parallel environment", International Journal of Distributed Sensor Networks, 2013, doi: 10.1155/2013/281707.

G. Yang and S. Liu, "Distributed cooperative algorithm for k-M set with negative integer k by fractal symmetrical property", International Journal of Distributed Sensor Networks, 2014, doi: 10.1155/2014/398583.

Relative Articles

Supplements(0)

Cited By

Proportional views