Is the Mandelbrot set computable?

Hypercomputing the Mandelbrot Set?

The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the (non-)computability of the set. It considers two models of decidability over the reals (which are treated much more thoroughly and technically in [1], [2], [3] and [4] amon...

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

Generalized Binet dynamics

The Binet formula provides a mechanism for the Fibonacci numbers to be viewed as a function of a complex variable. The Binet formula may be generalized by using other bases and multiplicative parameters that also give functions of a complex variable. Thus, filled-in Julia sets that exhibit escape time may be constructed. Moreover, these functions have computable critical points and hence we can...

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...