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The sister paper[1] contains the fractal dimensions of some of the images using a boxcount paper. [1]: https://arxiv.org/pdf/2402.06184.pdf https://arxiv.org/p
by bluetintedfort 3y ago
The sister paper[1] contains the fractal dimensions of some of the images using a boxcount paper.
[1]: https://arxiv.org/pdf/2402.06184.pdf https://arxiv.org/pdf/2402.06184.pdf
- magicalhippo 3y agoAh I had a quick read before I went to bed last night, missed that bit, cheers.
- bob88jg 3y agoThanks!! I was also under the impression Fractals required self similarity and not just infinite detail but glad to have that misconception corrected! I think it probably stems from the fact that all the fractals, I have seen, for which the dimension can be analytically calculated do show obvious patterns of similarity at different scales.
- magicalhippo 3y agoSearching I stumbled over this paper[1], which I found interesting, on characterizing the fractal-ness of geological structures. They point out that the usual measure of fractal dimension, or capacity dimension[2], doesn't consider the physical size of the features and can thus be inaccurate. Instead they suggest using the information dimension[3], which is bounded by the capacity dimension. [1]: https://doi.org/10.1016/j.chaos.2018.05.008 https://doi.org/10.1016/j.chaos.2018.05.008 (full text available on that hub of science) [2]: https://mathworld.wolfram.com/CapacityDimension.html https://mathworld.wolfram.com/CapacityDimension.html [3]: https://mathworld.wolfram.com/InformationDimension.html https://mathworld.wolfram.com/InformationDimension.html
- tudorw 3y agoSeems there are a few more, Higuchi Dimension, Box Counting Dimension (D0), Generalized Rényi Dimension and others are discussed mid-way through this; https://medium.com/@h.a.papageorgiou/the-reality-of-the-ruliad-d9e7c9ef140d https://medium.com/@h.a.papageorgiou/the-reality-of-the-ruli...