0
votes
2answers
45 views

Mathematical background for one wishing to study Chaos/Complexity Theory

I don't have a very strong mathematics background. In fact I quite abhorred mathematics during my Middle/High School years. I'm currently applying for PhD programs in the field of literature as that ...
0
votes
1answer
42 views

Reference - formal characterization and analysis of Koch curve

I am studying the Koch curve but most resources I have seen do not describe the Koch curve formally and are similar to the Wikipedia page on the subject. For example, I have looked at books like ...
1
vote
1answer
75 views

Reference - Fractal Geometry

I am looking for textbooks or lecture notes about Fractal Geometry that reach an advance level on the topic and aren't just introductory.
0
votes
0answers
17 views

algorithm for traversing a fractal in a “maximally ordered” way

consider a multidimensional fractal that can be "traversed" in an arbitrary order. is there an algorithm for traversing a fractal in a "maximally ordered" way? in other words the algorithm has ...
5
votes
1answer
56 views

Reference for a Cantor set in the plane formed from series of roots of unity

This is a long shot, but I'm looking for a particular article that I once read, and I'm trying to find it again. It deals with a certain Cantor set in the plane. The set could be written as something ...
7
votes
1answer
415 views

Self Study of Fractals

I am looking for a book to self-study fractals with a certain criteria. I have checked out Getting Aquainted with Fractals. Note that Getting Aquainted with Fractals does not include ...
8
votes
0answers
250 views

Kakeya Needle problem video

I'm intruiged by the Kakeya Needle problem, described here on Wikipedia. Wikipedia has a nice animation of a needle turning through a hypo-cycloid: What I'm searching for is a visualisation of the ...
4
votes
2answers
97 views

Good sources on studying fractals (the mathematical, and not just the pretty pictures version)?

Particularly, I'm interested in learning about the dimensions (whether it's always possible to find them, and if so, a concrete way of calculating them) of different types of fractals (given by the ...
2
votes
1answer
148 views

Heighway dragon and twindragon relation

The Heighway dragon F is defined as the limit set for the iterated function system $\begin{cases}f_1(z)=\frac{1+i}2 z\\f_2(z)=1-\frac{1-i}2z\end{cases}\quad$ starting from the two points 0 and 1. The ...
22
votes
5answers
334 views

Fractals reference

I want to present an elementary lecture about Fractals in the Nature. So, I am searching open or online references with good pictures like the following one: I prepared a good program that makes ...
5
votes
1answer
308 views

Hausdorff Dimension of Arbitrary Julia Set

I am looking to find an exact solution to the Hausdorff dimension of a Julia set $J(f)$ for a polynomial $f: z \mapsto z^2 +c$ given an arbitrary $c$. I know this question is known for a number of ...
27
votes
5answers
736 views

Why does the Hilbert curve fill the whole square?

I have never seen a formal definition of the Hilbert curve, much less a careful analysis of why it fills the whole square. The Wikipedia and Mathworld articles are typically handwavy. I suppose the ...
4
votes
3answers
509 views

Need good material on multifractal analysis

I'm searching for some good reading material on multifractal analysis. Preferably something accessible that doesn't put the stress too much on mathematical proofs but rather on applications. As long ...
11
votes
1answer
244 views

Reconstructing a Monthly problem: tree growth on the 2D integer lattice

I'm trying to reconstruct a problem I saw in the Monthly, years ago. Perhaps it'll look familiar to someone. In the integer lattice in the plane, we grow a tree in the following natural way: ...