Sierpinski Triangles and Carpets

thingiverse

This openSCAD code creates Sierpinski triangles and carpets. Learn about Sierpinski's work on Wikipedia or Wolfram Math. A helpful article is available at http://hmf.enseeiht.fr/travaux/CD9900/travaux/optmfn/hi/00pa/mfn03/champeau.htm, which explains how the Chaos Game generates Sierpinski triangles. The code produces 81 separate triangles that are subtracted from a single triangle to create an ornament with a hole for hanging, named Sierpinski_triangle.stl. Additionally, there are four STL files: Sierpinski_carpet.stl (a carpet after three cycles of iteration), Composite_carpet.stl (a composite of 3 carpets at different stages of iteration), Sierpinski_all.stl (a carpet where the central square is replaced by a triangle), and limited iterations due to openSCAD program limitations. Polymaker's (thing:8711) three-dimensional version of the triangle is attractive. These objects print well, with Sierpinski_carpet.stl possibly requiring a single shell and 50% infill for better printing quality.