Existence domain analysis and numerical algorithm of fixed point for generalized 3x+1 function T(x)

Tien Tzu Hsueh Pao/Acta Electronica Sinica

Volumn 39, Issue 10, 2011, Pages 2282-2287

  Liu, Shuai ^a   Che, Xiang Jiu ^a   Wang, Zheng Xuan ^a  

^a JILIN UNIVERSITY   (China)

Author keywords

Escape time; Existence domain; Fixed point; Fractal; Generalized 3x+1 function; Numerical algorithm

Indexed keywords

DOMAIN ANALYSIS; ESCAPE TIME; EXISTENCE DOMAIN; FIXED POINT; FIXED POINTS; FRACTAL IMAGES; NUMERICAL ALGORITHMS; NUMERICAL EXPERIMENTS; TRANSCENDENTAL FUNCTIONS;

FRACTALS;

ALGORITHMS;

EID: 81355134863     PISSN: 03722112     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. Alves J F, Graca M M, Dias M E S, et al. A linear algebra approach to the conjecture of Collatz[J]. Linear Algebra and Its Applications, 2005, 394(1): 277-289.
2. Lagarias J C. The 3x+l problem and its generalizations[J]. American Mathematical Monthly, 1985, 92(1): 3-23.
3. John Simons, Benne de Weger. Theoretical and computational bounds for m-cycles of the 3n+1 problem[J]. Acta Arith, 2005, 117(1): 51-70.
4. Mandelbrot B B. The Fractal Geometry of Nature[M]. San Fransisco: Freeman W H, 1982. 1-122.
5. LI Jin-jiang, ZHANG Cai-ming, FAN Hui, et al. Image inpainting algorithm based on fractal theory. Acta Electronica Sinica. 2010, 38(10): 2430-2435. (in Chinese)
6. YU Lu, WU Le-nan. Matrix representation and convergence analysis of fractal image encoding[J]. Acta Electronica Sinica. 2004, 32(7): 1103-1107. (in Chinese)
7. Pe J L. The 3x+1 fractal[J]. Computers and graphics, 2004, 25(3): 431-435.
8. Dumont J P, Reiter C A. Visualizing generalized 3x+1 function dynamics[J]. Computers and Graphics, 2001, 25(5): 553-595.
9. WANG X Y, YU X J. Study the dynamic theory of generalized 3x+1 function based on fractal visual method[J]. Progress in Natural Science, 2007, 17(4): 529-535. (in Chinese)
10. WANG Ze-ke. An efficient algorithm for computing the zeros of transeendental functions in the complex plane[J]. Acta Universitatis Sunyatseni, 1981. 15-21. (in Chinese)
11. Yunliang Long, Edward K N Yung. Kuhn algorithm: ultraconvenient solver to complex polynomial and transcendental equations without initial value selection[J]. International Journal of RF and Microwave Computer-Aided Engineering, 2002, 12(6): 540-547.
12. LIU Shuai, WANG Zheng-xuan. Fixed point and fractal images for a generalized approximate 3x+1 function[J]. Journal of Computer-Aided Design & Computer Graphics, 2009, 21(12): 1740-1744. (in Chinese)