Alright so for my work i am in the need of a Fractal with a spherical shape. Now, i have implimented a way to generate Fractals using a set of Equations. But so far i couldnt find a comprehensive source looking into Fractals which are to some extend or another spherical.
I do know that at N values tending to 1, something like the Julia set is a sphere. But it dosnt have any fractal features, its just a sphere.
Ideally i would want something like this: https://www.flickr.com/photos/syntopia/6854195470/in/photostream
Now the guy how made this did explain how, and he essentially just projected a 2D Fractal onto a 3D Surface and extruded it. Which wont work for my intended goal.
Something like this would be ideal:
But even here, to me, this dosnt look very 3D and more like a projection.
So to recap, i am looking for either a resource or set of equations which create Fractal geometry that has an overall spherical shape. If that is even a thing. Judging by how little there is on the subject i wouldnt be supprised if this is some sort of imposibility.
Thank you for reading and any help ! :D
The most promising tool seems to be Incendia, since it creates real fractals and not only projections.
Whether you can get at the algorithms is not immediately apparent, but possibly you get an idea of the principle behind them.
This arXiv paper entitled "Self-similar space-filling sphere packings in three and four dimensions" by Stäger and Herrmann provides some algorithm that might go into the direction you want:
Another possibly relevant paper is "Sphere inversion fractals" by Jos Leys:
Following literature on this topic lead me to the following papers too: