Questions tagged [fractals]

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Motion on fractal media

Can physical quantities such as displacement and velocity be defined for a body moving in fractional dimensions? For a point particle, the distance/displacement between any two points would be ...
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1answer
73 views

Is there a relation between this function and black holes?

I was fiddling with this complex function visualizer and accidentally found this function which looks a lot like the blackhole visualizations that I see on the net: $$ f(z)=(z\bar{z}-1)^z $$ and I'm ...
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1answer
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How to calculate fractal dimension by fitting on a log-log plot?

I have simulated a DLA pattern by MC method and the data is for fractal dimension. The right column is the number of particle N(r) into radius r and the left column is the radius r. I plotted a log-...
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1answer
37 views

Application of Correlation Dimension to Fractals other than Sets of Points

In Chaos Theory, the Correlation Dimension is defined to calculate the dimension of fractals. At least in the context where I've learnt it, it is applied to fractals made up of sets of points. Is it ...
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How to justify studies on fractal cosmology?

What are the arguments (theoretical and experimental) to support or to justify a fractal distribution of matter on all scales in cosmology? I see only one justification: On some small scales, matter ...
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Particle statistics in fractal dimensions? [closed]

We know that fermions and bosons are the only two (indistinguishable) particle statistics for $d\geq 3$, and that anyons are for $d=2.$ What if the space were a fractal? Like the Sierpinski gasket, ...
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Are quasicrystals always self-similar?

The diffraction patterns of quasicrystals very often display self-similarity ie. similarity under length scaling, thus relating them to fractals. My question is: Do they always display self-...
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1answer
68 views

Entropy of natural networks [duplicate]

How does one define the entropy of a natural network (say for example, a river network, or a morphological skeletal network of a lake in the figure below) ? For example, the following report suggests ...
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67 views

Intuition behind non-local stress tensor

Starting from the following Reisz Fractional Integro-differential formula (see for example https://www.amazon.com/Fractional-Integrals-Derivatives-Theory-Applications/dp/2881248640, chapter 25) $$ I^{...
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1answer
28 views

Difference between a strange chaotic and a strange non-chaotic attractor [closed]

Both of them look the same, but the SNA doesn't have positive lyapunov coefficients. What is the difference between them in terms of their attributes. A non-mathematical answer please
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1answer
122 views

Physical interpretation of power law cluster size distribution in percolation problem

In the site percolation problem, when the occupation probability $p \rightarrow p_c$, where $p_c$ is the critical probability. The characteristic length diverges, and assuming the usual scaling ansatz ...
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3answers
396 views

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 ...
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1answer
119 views

Sub-diffusive processes and fractional derivatives.

Are fractional derivatives an empirical fact of transport in complex media or is there a theoretical understanding behind it? Why do fractional derivatives describe sub diffusive processes? Why do ...
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1answer
388 views

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 ...
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1answer
140 views

Fractal structure in colloidal systems

In describing the configuration of a colloidal system, one often deals with either, disordered fluid states, disordered jammed states or crystalline states (so an underlying lattice structure), but in ...
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2answers
115 views

Can we calculate some of the main properties of lightning? [closed]

I've always been really interested in lightning. It's so cool, yet it's never really discussed in depth in typical physics courses. How do you calculate some of the basic properties of lightning? For ...
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1answer
65 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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1answer
230 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 ...
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1answer
1k 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 ...
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2answers
871 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-...
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4answers
423 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 ...
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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. ...
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1answer
367 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 ...
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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 ...
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1answer
71 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-...
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3answers
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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, using ...
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1answer
80 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?
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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 ...
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1answer
806 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 ...
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80 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?
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3answers
4k 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 ...
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1answer
125 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 first....
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0answers
111 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 ...
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1answer
350 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 ...
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1answer
2k 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....
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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 ...
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1answer
341 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 ...
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2answers
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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 ...
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2answers
579 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 ...
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1answer
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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 ...
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1answer
318 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 ...
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1answer
128 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 $q$ ...
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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 ...
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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 ...
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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 ...
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1answer
177 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)