A Mandelbrot Set whose Boundary is Piecewise Smooth
نویسندگان
چکیده
منابع مشابه
Is the Mandelbrot set computable?
We discuss the question whether the Mandelbrot set is computable. The computability notions which we consider are studied in computable analysis and will be introduced and discussed. We show that the exterior of the Mandelbrot set, the boundary of the Mandelbrot set, and the hyperbolic components satisfy certain natural computability conditions. We conclude that the two–sided distance function ...
متن کاملThe Mandelbrot set is universal
We show small Mandelbrot sets are dense in the bifurcation locus for any holomorphic family of rational maps.
متن کاملGroups whose set of vanishing elements is exactly a conjugacy class
Let $G$ be a finite group. We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$. In this paper, we classify groups whose set of vanishing elements is exactly a conjugacy class.
متن کاملHypercomputing 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...
متن کاملThe Mandelbrot Set as a Modular Form
An exploration of the interior or the Mandelbrot Set and the appearance of functions appearing to be similar to modular forms. This provides yet another example of the close interconnection between the structure of the Modular Group SL(2,Z) and fractals. The relationship is demonstrated computationally and visually, and not from first principles; visually, the interior resembles the Weierstrass...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1989
ISSN: 0002-9947
DOI: 10.2307/2001299