Shrubs in the Mandelbrot Set Ordering

Chaotic bands in the Mandelbrot set

Hyperbolic components and Misiurewicz points of the chaotic region of the Mandelbrot set are located in what we call shrubs. Each shrub has two well-differentiated parts. The first one, shrub0; corresponds to the main branch of the shrub. The second one, shrubr; corresponds to all the other branches of the shrub. In this paper, we have focused on the ordering of the hyperbolic components and Mi...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Visualizing bivariate long-tailed data

Variables in large data sets in biology or e-commerce often have a head, made up of very frequent values and a long tail of ever rarer values. Models such as the Zipf or Zipf–Mandelbrot provide a good description. The problem we address here is the visualization of two such long-tailed variables, as one might see in a bivariate Zipf context. We introduce a copula plot to display the joint behav...

A Generalized Mandelbrot Set Based On Distance Ratio

The iteration of complex function can generate beautiful fractal images. This paper presents a novel method based on the iteration of the distance ratio with two points, which generates a generalized Mandelbrot set according to distance ratio convergence times. This paper states the definition of distance ratio and its iteration. Then taking the complex function f(z)=z+c for example, it discuss...

Dynamics of Mandelbrot Set with Transcendental Function

These days Mandelbrot set with transcendental function is an interesting area for mathematicians. New equations have been created for Mandelbrot set using trigonometric, logarithmic and exponential functions. Earlier, Ishikawa iteration has been applied to these equations and generate new fractals named as Relative Superior Mandelbrot Set with transcendental function. In this paper, the Mann it...