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I want to model a spiral mathematicaly like this:

A spiral like that of the 3d spiral of a single planetary motion through space except I want the trajectory of it (the direction of the spiral running through its center) to be also a larger spiral which is also part of another larger spiral etc and so ultimately my question is...

Is there a formula to describe a spiral that forms a spiral Infinitum, a fractal-like spiral geometry that repeats infinitely inward and outward? Thus the spiral has no radial tube size, as it is a mathematical line that when zoomed in on is also a spiral...

I hope this is clear? Any help appreciated and if this is old news would be great to be pointed to the maths...

thanks!

Jean Marie
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Andromodea
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  • What do you mean by 3D spiral ? Don't you mean a "helix" (that can be drawn on a cylinder) ? – Jean Marie Feb 22 '21 at 09:43
  • https://fractalforums.org/noobs-corner/76/infinite-helix-distance-estimator-helix-from-helix-from-helix-from-helix/3873/msg25115#msg25115 discussion https://fractalforums.org/index.php?action=gallery;sa=view;id=5352 image https://github.com/claudeha/fragm-examples/blob/d0e7f53b372fe84d22a2bf3e6cc0a2fd7de9fcab/00-Helices.frag#L33-L60 code. I once constructed a distance estimator (extending in one direction only, to finite depth) with each layer visible as a tube. It's based on cutting a stack of toruses and sliding the cut along so neighbouring toruses line up. – Claude Feb 22 '21 at 10:18
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    Is this of interest for you ? – Jean Marie Feb 22 '21 at 10:54
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    No reaction to the comments we have made ? Consider that this site is based on dialog. Don't await a "served on a silver tray" answer... – Jean Marie Feb 23 '21 at 16:31
  • Awesome! Yes, thank you, Jean Marie, Claude. Apologies for the delay in response, I appreciate your replies. I'll have a look at what you have linked for me. ps - I'm a new at this you may have guessed, I meant helix, thanks again! – Andromodea Feb 25 '21 at 08:07

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