Multiplier Periodic Buds of Complex Mapping f(z,c)=z~(-2)+c
Song Chun
Abstract
Song Chun
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 superattracted 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 superattracted points is proposed based on lots of experiments. A novel algorithm of constructing wordlifting formula is presented. The accurate solution of superattracted 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.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
?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 superattracted 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 superattracted points is proposed based on lots of experiments. A novel algorithm of constructing wordlifting formula is presented. The accurate solution of superattracted 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