Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 653816, 12 pages
Research Article

Accurate Computation of Periodic Regions' Centers in the General M-Set with Integer Index Number

College of Computer Science and Technology, Dalian University of Technology, Dalian 116024, China

Received 27 October 2009; Revised 24 February 2010; Accepted 7 June 2010

Academic Editor: Recai Kilic

Copyright © 2010 Wang Xingyuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents two methods for accurately computing the periodic regions' centers. One method fits for the general M-sets with integer index number, the other fits for the general M-sets with negative integer index number. Both methods improve the precision of computation by transforming the polynomial equations which determine the periodic regions' centers. We primarily discuss the general M-sets with negative integer index, and analyze the relationship between the number of periodic regions' centers on the principal symmetric axis and in the principal symmetric interior. We can get the centers' coordinates with at least 48 significant digits after the decimal point in both real and imaginary parts by applying the Newton's method to the transformed polynomial equation which determine the periodic regions' centers. In this paper, we list some centers' coordinates of general M-sets' k-periodic regions (k=3,4,5,6) for the index numbers α=25,24,,1 , all of which have highly numerical accuracy.