Sierpinski pyramide - without the need of support

by apal, published

Sierpinski pyramide - without the need of support by apal Dec 15, 2013
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This thing design features some Sierpinski pyramides that could be printed without any support structure. In each depth of the pyramide, there are 5 sub-pyramides while the central-upper one is supported by (a non-fractal) upside-down pyramide with the same size. Hence, it can easily be printed and the result will look very nice (see image), and real-world light-shade effects practically "hide" these supporting pyramides.

You may able to generate any version for this using the C code attached. See Instructions for further details.


One just has to print the designs without any kind of further tuning or so. First, this design has been printed without any kind of support base (see the file sierpinski_what_is_seen_on_thepic.stl). However, some printer drivers (such as CURA what we are using with UltiMaker) prints the individual smallest triangles on the base individually instead a fully filled square. Therefore, it was very hard to remove the object from the printer after the printout has been completed and smallest pyramides could likely break. Due to this side-effect, the generator program has been modified in order to add a support base with one unit of smallest-pyramide-height. This support can clearly be seen on the attached sierpinski??mm_d?.stl files.

Sierpinski pyramide is also a fancy thing to demonstrate STL format: facelets are purely triangles (with the exception of the base) and STL encodes triangles as well. With this design, a C code is shipped (see the *.zip file, with pre-compiled Linux and Windows binaries), with which you can create arbitrary Sierpinski pyramides. And one can teach how recursive algorithms work. See the command line option ./sierpinski --help (on Linux) or sierpinski.exe --help (on Windows) for more instructions.

Please note that the Windows binary has only be compiled on a Linux machine using the 32-bit version of the MinGW cross-compiler. But it should work as well on Win* systems as well.

Also note that by default, this sierpinski.c code prints its output to the standard output -- that can be a lot since there are lots of pyramides and triangles. So redirect it to a file or use the -o ... option.

What is your smallest size-to-2^depth ratio what your printer can print nicely? ;)

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annyi :)

Thanks for adding this design! Printed the 20mm version on a Printrbot 2014 Simple.

It's still a perfect fractal, you know, just not a perfect Sierpinski :) If anything you've made your own unique fractal.

It has a finite (non-zero) volume, unlike the original sierpinski. But otherwise, yes, it's a fractal in total ;) i just mentioned in the description that the supporting upside-down pyramides are non-fractals, just a block of material.

I used PLA, and it seems that if the smallest triangles 2mm or larger, then it's okay. Also tried with 10mm/depth3, that is 1.25mm per triangle side, which also looks nice but bit confuse.

Hah, I'd like to see you try and print something with ZERO volume ;)

Looks like triforces, so i'm printing it :)

scratch that my slicer consistently fails to slice it properly, I get some weird shape out of it. netfabb cloud didn't help

apal - in reply to

In CURA, these work nicely w/o any trick (i'm just printing the 20mm/depth3 now for a quick test). However, freecad uses to worry about some mesh problems when i open these *.stl's. I do not really understand why (maybe it is a bug in freecad?) but might be related... who knows? a