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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:

enter image description here

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

ErikHall
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  • Perhaps this discussion over on mathematica.statckexchange might help: https://mathematica.stackexchange.com/questions/15047/ – Mark McClure Mar 09 '22 at 09:55

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The most promising tool seems to be Incendia, since it creates real fractals and not only projections.

enter image description here

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:

enter image description here

Another possibly relevant paper is "Sphere inversion fractals" by Jos Leys:

enter image description here

Following literature on this topic lead me to the following papers too:

  • "The Fractal Dimension of the Apollonian Sphere Packing" by Borkovec and Paris
  • "A generalization of the spherical inversion" by Ramírez and Rubiano
Eldar Sultanow
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    The paper seems very much like what i need. But sadly i dont have that much time. However the software you linked might be even better. It has some user generated Fractals which always provide the equations. So.... that is useful :D Thank you very much ! – ErikHall Mar 06 '22 at 20:02
  • Great, I am glad if this is helpful for you. – Eldar Sultanow Mar 06 '22 at 20:05