Sierpinski Triangles and Carpets
8
Likes
599
Downloads
904
Views
Published on November 16, 2012
Derived from
Sierpinski Pyramid
by polymaker
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:
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Sierpinski_all.stl is a carpet where the central square has been replaced by a triangle.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.
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Sierpinski_all.stl is a carpet where the central square has been replaced by a triangle.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.
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.
License
Sierpinski Triangles and Carpets by pmoews is licensed under the Attribution - Creative Commons license.
ok dxf posted - Sierpinski.carpet.dxf is properly scaled