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2
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1answer
40 views

High surface area for given volume [closed]

What can be a example similar to mathematical Koch flake that could be found in nature... where for a given enclosed volume its surface area is indefinitely large?
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0answers
8 views

Power scaling behavior in Detrended Fluctuation Analysis

I am trying to apply DFA in my time-series, however, remain the the determination linear relationship of the log fluctuation vs. log scale plot i.e. slope which indicates to the power scaling behavior ...
7
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0answers
94 views

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 ...
1
vote
1answer
180 views

Is the double pendulum an example of a strange attractor?

Imagine a pendulum to which is attached another one (not necessarily the same length). Does this pendulum, when you let it go (which can be done in many ways but let's keep the total potential ...
1
vote
2answers
71 views

Self similar functions

I'm trying to undestand the self-similarity as an invariance of a function under certain transformation. For example I think $$f(\lambda x)=\lambda^\epsilon f(x)$$ could be understood as a self-...
1
vote
3answers
156 views

Can a particle have no instantaneous velocity at all points of the path taken but a finite average velocity?

I have a question on kinematics. Say the path traced by a particle is given by a Koch curve or Koch snowflake. Now consider the particle starts from some arbitrary point $A$ on the curve and ...
0
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0answers
27 views

Systems with elements having size which tends to zero

[Question] If I have an element whose size(as in physical dimensions) tend to 0 but is NOT 0 (very very very small). If I create a system from these elements based on (say) the fractal concept (...
4
votes
1answer
129 views

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. ...
1
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0answers
72 views

How do I apply a renormalization technique to estimate the fractal dimension of a diffusion limited aggregate?

Diffusion Limited Aggregation (DLA) is an interesting phenomena observed in nature and discussed here. From a theoretical view point, it'd be nice to know about the fractal dimension of a DLA formed ...
0
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1answer
54 views

I'm interested in the use of self-similarity in physics. Is this a reputable subject? [closed]

I'm interested in fractals, self-similarity, and chaos. Many physicists disregard these phenomena as candidates to explain the fundamental properties of the universe. However, when I read about ...
2
votes
1answer
58 views

Any fractal physical model that generates time series which demonstrate heavy-tailed (non-Gaussian) behavior in some form?

I know that fractal structures have power-laws in various forms "hidden" in them. I am looking for the most simple fractal model that I can find that generates time series with, say, Pareto-...
5
votes
3answers
767 views

What are the technical obstructions that prevent scale relativity from being a viable theory of quantum-gravity? [closed]

This post has been imported on physicsoverflow, see here. The astrophysicist Laurent Nottale develops since 1984 the scale relativity, which aims to unify quantum physics and relativity theory, ...
0
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0answers
20 views

Detrended Fluctuation Analysis

In the fitting procedure of DFA, how can we understand which order of DFA (Detrended Fluctuation Analysis) (DFA1, DFA2, and higher order DFA) should be applied in the time series?
6
votes
2answers
150 views

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 ...
10
votes
1answer
314 views

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 ...
1
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0answers
61 views

Why is there roughness on every surface?

Why is there roughness on every surface? I think a smooth surface could better minimize the surface energy. Besides, why does the roughness happen to be fractal?
2
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3answers
1k views

Non-linear dynamics vs Chaos

I am confusing between non linear dynamics and chaos. Chaos is also a non-linear dynamics right? then what is the difference between chaos and non-linear dynamics? What I understood about chaos is ...
1
vote
1answer
115 views

Minimum amount of fluid to experience turbulence?

Turbulence is a challenge to model and simulate: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the ...
2
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0answers
97 views

Spin-statistics theorem on spaces with non-integer dimensions

What would be the spin-statistics relation for particles in a space with non-integer dimension, $ 2 \lt D \lt 3 $? In other words (cf. stackexchange questions here and here), what is the first ...
4
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0answers
141 views

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 ...
4
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1answer
1k views

“windows of order” in the Bifurcation diagram

When looking at the bifurcation diagram of a chaotic system, one observes "windows of order", namely short intervals where the system briefly leaves its chaotic state and then rapidly returns to chaos....
11
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2answers
915 views

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 ...
4
votes
1answer
208 views

Are there real life applications for Hausdorff dimensions, specifically crack formations?

I was curios about Hausdorff dimensions. They seem to neatly describe rough surfaces. So I was wondering if there are common applications of Hausdorff dimensions in things like complicated friction ...
2
votes
1answer
2k views

Why do fractal systems show power-law behavior?

I'm not sure I quite understand why systems with fractal systems show power-law behavior. My "gut" understanding is that the power-law index indicates the correct scaling factor for the system so that ...
3
votes
2answers
374 views

Do we live in an integer dimension?

I have read that there exist non-integer fractal dimensions and the images generated from these dimensions look organic and they seem to provide a new way of describing the world around us, which ...
9
votes
1answer
892 views

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 ...
2
votes
1answer
249 views

Fractal Cosmology and Misner's Chaotic Cosmology

I have a question pertaining to the ideas behind the considered homogeneity and isotropic nature of the universe (at a grand scale) versus the theory of a chaotic and anisotropy structure of the ...
9
votes
1answer
98 views

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 $q$ ...
5
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1answer
732 views

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 ...
6
votes
3answers
789 views

If the universe were a fractal

Inflation seems to solve many of the problems of cosmology like horizon problem, flatness problem etc. Now suppose, I am a devil's advocate and tries to find holes in this beautiful theory. I argue ...
1
vote
1answer
162 views

Current Physical Applications of Elastic Fractals

Are there any known uses of modeling with elastic fractals in current physical applications? (Especially uses concerning with self-similarity)