Sierpinski Triangles and Carpets

thingiverse

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 Sierpinski_all.stl is a carpet where the central square has been replaced by a triangle.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