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

Ah I had a quick read before I went to bed last night, missed that bit, cheers.

Thanks!! 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.

Searching 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 (full text available on that hub of science)

[2]: https://mathworld.wolfram.com/CapacityDimension.html

[3]: https://mathworld.wolfram.com/InformationDimension.html

Seems 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-ruli...