2003Journal of Northeastern UniversityRequires access

Multiplier Periodic Buds of Complex Mapping f(z,c)=z~(-2)+c

Song Chun

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Abstract

?Julia set is a kind of Mandelbrot set which follows the rules of uncountable,limited and infinite nesting. Using escape time algorithm, the Julia sets' fractal image is protracted on the multiplier periodic superattracted points of complex mapping f(z,c)=z-2+c. It is found that there is a tight relation between the Mandelbrot set and Julia set. The rule of constructing symbol sequence on arbitrary multiplier periodic superattracted points is proposed based on lots of experiments. A novel algorithm of constructing wordlifting formula is presented. The accurate solution of superattracted points on principal axis and the immovable point of Julia set is obtained. It is also found that there are two general constants of Julia set. The constants are validated on the nonprincipal axis.

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?Julia set is a kind of Mandelbrot set which follows the rules of uncountable,limited and infinite nesting. Using escape time algorithm, the Julia sets' fractal image is protracted on the multiplier periodic superattracted points of complex mapping f(z,c)=z-2+c. It is found that there is a tight relation between the Mandelbrot set and Julia set. The rule of constructing symbol sequence on arbitrary multiplier periodic superattracted points is proposed based on lots of experiments. A novel algorithm of constructing wordlifting formula is presented. The accurate solution of superattracted points on principal axis and the immovable point of Julia set is obtained. It is also found that there are two general constants of Julia set. The constants are validated on the nonprincipal axis.

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Available abstract

?Julia set is a kind of Mandelbrot set which follows the rules of uncountable,limited and infinite nesting. Using escape time algorithm, the Julia sets' fractal image is protracted on the multiplier periodic superattracted points of complex mapping f(z,c)=z-2+c. It is found that there is a tight relation between the Mandelbrot set and Julia set. The rule of constructing symbol sequence on arbitrary multiplier periodic superattracted points is proposed based on lots of experiments. A novel algorithm of constructing wordlifting formula is presented. The accurate solution of superattracted points on principal axis and the immovable point of Julia set is obtained. It is also found that there are two general constants of Julia set. The constants are validated on the nonprincipal axis.

Key concepts: Julia set, Mandelbrot set, Mathematics, Periodic point, Multiplier (economics), Newton fractal, Cantor set, Uncountable set

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