All Questions
4
questions
1
vote
0
answers
124
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How many two-dimensional space filling Hilbert-like curves are there?
I'm interested in filling 2d square with space filling, non-self-intersecting, locality preserving, self-similar curves, like Hilbert curve. I found interesting work concerning three dimensional case ...
- 355
4
votes
3
answers
1k
views
Is there an (almost) dense set of quadratic polynomials which is not in the interior of the Mandelbrot set?
For the parameter plane of complex quadratic polynomials, $(z\mapsto z^2+c)_{c\in\mathbb{C}}$ :
Is it possible to find a part of the parameter plane, scanned with a given limited precision (...
- 445
3
votes
1
answer
230
views
Contractibility of connected holomorphic dynamics?
Let $f$ be a function, holomorphic in $\mathbb{C}$, and $K(f)$ its non-escaping set :
$$K(f) = \{ z \in \mathbb{C} : f^{(k)}(z) \nrightarrow_{k \to \infty} \infty \} $$
Question : If $K(f)$ is ...
- 25.5k
13
votes
1
answer
2k
views
Analysis of the boundary of the Mandelbrot set
Motivation: The Mandlebrot set is a simply connected set with an infinitely complex boundary, but CAN one move from interior to the exterior of this topological space by just crossing over a finite ...
- 841