A a never-ending pattern, infinitely complex and self-similar across different scales. It is created by repeating a simple process recursively.
Questions tagged [fractals]
67 questions
22
votes
9 answers
Is there such a thing as a "physical" fractal?
The recent discovery of a molecule that mimics the Sierpinski gasket has spurred headlines identifying it as the first fractal scientists have found in nature. I find these claims highly dubious because it's either entirely impossible for a real…
starseed_trooper
- 452
19
votes
2 answers
Literature on fractal properties of quasicrystals
At the seminar where the talk was about quasicrystals, I mentioned that some results on their properties remind the fractals. The person who gave the talk was not too fluent in a rigor mathematics behind those properties, and I was not able to find…
Misha
- 3,387
16
votes
2 answers
Link between anomalous dimensions and fractal dimensions
I just realized that anomalous dimensions in quantum/statistical field theory is not that different from fractal dimensions of objects. They both describe how quantitaive objects transform under a scale transformation (renormalization group…
13
votes
2 answers
Calculate/Estimate the fractal dimention of the logistic map
This is the logistic map:.
It is a fractal, as some might know here.
It has a Hausdorff fractal dimension of 0.538.
Is it possible to calculate/measure its fractal dimension using the box counting method?
A "hand waving calculation" is good…
GuySoft
- 435
13
votes
1 answer
Why is it that fractal antennas can filter out so many frequencies?
As known, fractal antennas are used for example in cell phones. But why is it that so many different kinds of frequencies can be filtered out of the forest of radio waves surrounding us? Is it because of the self-similarity, when you look at…
Deschele Schilder
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12
votes
1 answer
Fractal nature of turbulence
Someone described to me the difficulty of numerically simulating turbulence as that as you look at smaller length scales you see more structure like you do in a fractal. Searching on google for 'fractal turbulence' does seem to bring up quite a few…
Ginsberg
- 488
12
votes
1 answer
How or why is fractional quantum mechanics important?
I read about Fractional Quantum Mechanics and it seemed interesting. But are there any justifications for this concept, such as some connection to reality, or other physical motivations, apart from the pure mathematical insight?
If there are none,…
resgh
- 1,184
10
votes
3 answers
Parametric equation for the electric field of a uniformly charged surface with a triadic Koch curve fractal perimeter
I'm currently studying fractals as well as electrodynamics. So, I thought why not create a problem using concepts from both subjects.
I want to study the electric field, at the centroid of the initial triangle, of a charge $q$ that's uniformly…
Mockingbird
- 1,228
10
votes
1 answer
Fractal patterns on water
I stored water in a bucket (of aluminium probably), and some random fractal-like patterns are formed on the water:
See here for some more pictures.
Why did this happen?
I'm unable to reproduce it. How can I reproduce it again? Just leaving it…
Excel Hand
- 101
- 4
10
votes
1 answer
Renyi fractal dimension $D_q$ for non-trivial $q$
For a probability distribution $P$, Renyi fractal dimension is defined as
$$D_q = \lim_{\epsilon\rightarrow 0} \frac{R_q(P_\epsilon)}{\log(1/\epsilon)},$$
where $R_q$ is Renyi entropy of order $q$ and $P_\epsilon$ is the coarse-grained probability…
Piotr Migdal
- 6,530
10
votes
1 answer
How would a fractal refract light?
A fanciful Pink Floyd reference has led me to wonder what white light passing through an object with an infinitely complex surface would do. Would it exit from a single chaotically-chosen point on the surface? Would it split into its constituent…
Colin P. Hill
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9
votes
1 answer
Physics-oriented books on fractals
I'm looking for some good books on fractals, with a spin to applications in physics. Specifically, applications of fractal geometry to differential equations and dynamical systems, but with emphasis on the physics, even at the expense of…
a06e
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8
votes
0 answers
Fisher exponent and fractal structure
In the context of critical phenomena, there are several critical exponents commonly used to characterize the singular behaviour at the point of phase transition. The Fisher exponent $\eta$ is defined through
\begin{equation}
C(T,x) = \frac{…
SaMaSo
- 538
8
votes
2 answers
Fractal dimensions: can anything be calculated with them?
Various exact algorithms and defining formulas have been devised for the calculation of parameters called 'fractal dimensions'. Practical applications of FD's are evaluation, comparison and classification of an amazingly wide range of natural…
Zaaikort
- 490
7
votes
4 answers
Where can I get an introduction to the mathematics behind Hofstadter's Butterfly?
Are there any good books that give good mathematical/physical background to the workings of the Hofstadter's Butterfly? I'd appreciate some references. Books or Public access papers will work.
Preferably, I'd like something that gives some insight…
Zach466920
- 1,137