braided epicycloid knots

thingiverse

Some experiments with parametrics "knots" based on epicycles pedal curves: http://mathworld.wolfram.com/EpicycloidPedalCurve.html . Connecting more than three knots to build a bidimensional continuous pattern (a kind of fabric) reveals a strong constraint: you can only connect a loop to another one, effectively eliminating the possibility of a simple surface filling pattern. Viewing the knots as triangles makes this clear. Exploring how much space I can fill with these knots naturally leads to the Sierpinski triangle; it simply emerges from trying to connect as many knots as possible. I'm attaching an OpenSCAD file (free software). The function that draws the knot is epi.