Filled Julia set

Fractal dimension is a measure of how fragmented of fractal object is. In fractal geometry, there are various approaches to… (More)

Building on recent work by Rippon and Stallard, we explore the intricate structure of the spider’s web fast escaping sets… (More)

In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present an… (More)

0 lies on a periodic orbit. We then perturb F0 by adding a pole at the origin. Our goal is to investigate the structure of the… (More)

We show that if a polynomial filled Julia set has empty interior, then it is computable. 

While most polynomial Julia sets are computable, it has been recently shown [12] that there exist non-computable Julia sets. The… (More)

The operation of “mating” two suitable complex polynomial maps f1 and f2 constructs a new dynamical system by carefully pasting… (More)

Let f : z 7→ z + c be a quadratic polynomial whose Julia set J is locallyconnected. We prove that the Brolin measure of the set… (More)

We prove that the only possible biaccessible points in the Julia set of a Cremer quadratic polynomial are the Cremer fixed point… (More)

is connected. Otherwise, it has infinitely many pieces. The Mandelbrot set is the set of cvalues for which the filled Julia set… (More)