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6
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2answers
127 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
155 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 ...
2
votes
0answers
55 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
votes
3answers
702 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
81 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
votes
0answers
89 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 ...
3
votes
0answers
103 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
votes
1answer
724 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 ...
9
votes
1answer
696 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
131 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
999 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 ...
2
votes
2answers
279 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 ...
10
votes
1answer
762 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
203 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
82 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
votes
1answer
544 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 ...
1
vote
1answer
145 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)