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Sierpinski Triangles and Carpets

by pmoews, published

Sierpinski Triangles and Carpets by pmoews Nov 16, 2012

Description

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Sierpinski_all.stl is a carpet where the central square has been replaced by a triangle.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

Recent Comments

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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.
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

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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.

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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