INFINITE-CORNER-POINT FRACTAL IMAGE GENERATION BY NEWTON METHOD FOR SOLVING EXP(-ALPHA-ZETA+Z/ZETA-Z)-1=0

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Newton's method is sensitive to an initial guess. It exhibits chaotic behavior that generates interesting fractal images. Most of them have either a finite number of attractors (attractive fixed points) or unbounded Julia sets. In this paper, we show that Newton's method for a family of equations exp(-alpha zeta + z/zeta - z) - 1 = 0 (for alpha > 0 and Absolute value of zeta = 1) has infinitely many attractors and a bounded Julia set. The dynamics of Newton's method for finding their roots are also visualized.
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Issue Date
1993
Language
ENG
Article Type
Article
Appears in Collection
CS-Journal Papers(저널논문)
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