Customizable Sierpinski tetrix

by owens, published

Customizable Sierpinski tetrix by owens Mar 3, 2014
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Customizable Sierpinski tetrix by owens is licensed under the GNU - GPL license.

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Continuing the theme of fractals that print with their own support structures, this is a model of the Sierpinski tetrix, a fractal based on the tetrahedron. It's a difficult object for a fused-filament printer because it involves lots of bridges, and the individual tetrahedra are only lightly connected to each other.

To make this model I started with cgranade's OpenSCAD Recursive Sierpinski Tetrahedron, which includes a clever adaptation for 3D printing, a parameter that adjusts the adhesion between adjacent tetrahedra. It makes the tetrix less like the mathematical ideal, but a perfect model isn't printable anyway.

I added external support that lets the model print upside-down, which solves the bridging problem. See the instructions for how to customize it and suggestions on how to get a good print.


The Customizer parameters are as follows:

  • Order - the level of recursion of the fractal. Zero is a solid tetrahedron, and the script will work up to 6, but I've limited it to 4 in Customizer to reduce the load on the servers because I don't think anything beyond that level is likely to be printable.

  • Size - the length of a side of the tetrix, but note that the size varies a little with different levels of recursion, and will need adjustment if you want exact results.

  • Adhesion - the adjustment (from cgranade's original code) that allows a connection between adjacent tetrahedra. I've found 0.25 to be a reasonable starting value, you can try setting it lower (less adhesion, but a more ideal fractal).

  • Intersection - the amount that the support structure overlaps with the tetrix. This is not in millimeters because it's applied before the scaling. At a size of 80 mm, 0.005 produces a solid structure that isn't too hard to remove.

I'd suggest starting with the defaults. Smaller prints may be possible but I've found that my printer inevitably knocks some of the small tetrahedra loose, and the print is ruined.

It's likely that the OpenSCAD output will need to be repaired before it can be sliced. For the example STL file, I used Netfabb Cloud.

I've had success with these parameters, and with the following settings in Slic3r:

0.30 mm layers
3 perimeters
3 top and bottom layers
avoid crossing perimeters
0% infill
0 solid layers
0 mm solid infill threshold area

This keeps the printer from spending too much time on each small tetrahedron, and seems to make the whole model more stable. The resulting print has 14 g of plastic in the finished tetrix and 21 g in the supports, but they're already quite minimal and I'm not sure how to make them smaller and still have them work.

To remove the supports it's best to hold the model gently but firmly and slowly rock the support back and forth, only bending it just a very small amount until the plastic begins to break loose. Other than that the model should need no cleanup.

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i edited the html so i can have it go beyond 4. I did 8 and it will probably look awesome.

EDIT: it wouldn't create it. add some more options so you can go beyond order 4

turned out superbly. Thanks for the great upload!

much Zelda, such triforce. wow.

I dont know what your talking about, but all I see is a giant triforce made out of smaller triforces

Feel free to Customize it, and name your version however you like ;)