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I can create a Menger sponge fractal using geometry nodes.

Image1:

im1a

im2a

See Blender file below:

Now I'm trying to create a Sierpinski Dodecahedron

Image2

I tried to replace the cube node with a Dodecahedron created as an object but that didn't work

Image3

The goal is to create the Sierpinski Dodecahedron fractal that can be sliced into several sections and 3D printed out.

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    $\begingroup$ Have been discussing this with @lemon just recently .. have got this far.. but running into floating-point errors in the dodecahedral case. Got to get the maths right for the scaling factor. And I know, on my machine, if I go one level further I will crash $\endgroup$
    – Robin Betts
    Nov 20, 2021 at 20:13

2 Answers 2

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with this node setup:

enter image description here

you get this:

enter image description here

one more instance level:

enter image description here

enter image description here

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    $\begingroup$ Great stuff! How did you determine your scale factor? I wound up with accumulating deviations.. (Mind you, the resolution will surely be greater than any printer's, anyway...) $\endgroup$
    – Robin Betts
    Nov 21, 2021 at 8:17
  • $\begingroup$ Thank you!!!!! I just read the wiki article 😅 $\endgroup$
    – Chris
    Nov 21, 2021 at 8:31
  • $\begingroup$ One more level and my computer still worked but Blender crashed everytime…😢 $\endgroup$
    – Chris
    Nov 21, 2021 at 8:32
  • $\begingroup$ :) I thought I'd read the right wiki article.. but apparently not... link? I think we still both have a problem... coincident (duplicate) instances ?? .. you could maybe squeeze another level out.. $\endgroup$
    – Robin Betts
    Nov 21, 2021 at 8:53
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    $\begingroup$ that gives the scale factor for instances in the corners: 1/(2+phi) I've still got to work out the factor for instances on the corners? I'll get to it.. my neurons aren't firing atm. Need coffee. $\endgroup$
    – Robin Betts
    Nov 21, 2021 at 10:05
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test

test2

This setup works for every fractal. The current scale factor (the Value and its Math node) is set to scale dodecahedrons, but it can be adjusted for other primitives (usually you would change the Power to a Multiply).

To anyone who wants to render this, I recommend 3.0.1, because more recent versions cause artifacts with overlapping geometry (it's a known regression).

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