The fractals tag has no wiki summary.
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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 $q$ ...
9
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1answer
352 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 ...
4
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1answer
53 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
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2answers
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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 ...
2
votes
1answer
98 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
1answer
92 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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0answers
77 views
Help with Chaos theory! I need an investigation topic [closed]
I'm about to undertake a potentially torturous journey. I'm a part of the ib diploma program (a program for high school students) and as a requirement I have to write a 4000 word essay about a subject ...
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0answers
43 views
Terminology Fractional Physics [closed]
I recently read an article about the use of physics in computer graphics. Moreover, the method of "fractional Physics" used to provide the awesome three dimensional effects we've come to enjoy. My ...
