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Sierpinski Triangles and Carpets

by pmoews, published

Sierpinski Triangles and Carpets by pmoews Nov 16, 2012
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Summary

Here is openSCAD code to make Sierpinski triangles and carpets. You can read about Sierpinski's work on Wikipedia or Wolfram Math. I like the article by Sylvie Champeaux at:

http://hmf.enseeiht.fr/travaux/CD9900/travaux/optmfn/hi/00pa/mfn03/champeau.htm

which explains how the Chaos Game leads to a Sierpinski triangle.

Sierpinski_triangle.stl is an ornament with a hole for hanging. The openSCAD code produced 81 separate triangles which were subtracted from a single triangle to make the ornament.

Sierpinski_carpet.stl is a carpet after three cycles of iteration.

Composite_carpet.stl is a composite of 3 carpets at different stages of iteration.

Sierpinski_all.stl is a carpet where the central square has been replaced by a triangle.

The triangles and carpets are limited to 3 or 4 iterations here; attempts to go further ran into openSCAD program limitations. Note that Polymaker, (thing:8711), has created an attractive three dimensional version of the triangle.

Instructions

These objects are easily and quickly printed with or without a raft.

Sierpinski_carpet.stl has the smallest features and perhaps prints better with a single shell and 50% infill. The smallest squares had to be made larger than is required by the generating algorithm so as to be properly sized by ReplicatorG.

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ok  dxf posted - Sierpinski.carpet.dxf is properly scaled

Can you also post DXF files of these.. ??  For us poor folk with laser engravers?  Thx

You can make a DXF by using the projection() call. This will probably take forever and a day as the projection() function isn't super efficient. That will create a 2D shape that can be exported as a DXF.

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