I’ve seen my nine years old son drawing this geometry on a squared notebook. He saw my interest and simply told me “mummy, I can show you how to draw it” and repeated the sequence of segments just for me. I started being captured by the sequence, the 2D geometry, the symmetry and I imagined it as a 2D projection of an “8” shaped spiky knot. I have always been fascinated by knots, especially as patterns, like the celtic motifs. This triggered me now as a 2D/3D designer and I came up with decomposing the shape in simple repeated elements to be reproduced as an array (copied, mirrored, turned).
With FreeCAD, first I drew the basic geometry elements as two sketches
and repeated them in arrays with the same distance between elements.
Then, mirroring the left array symmetrically on the other side of the “S” shaped one , I could easily reproduce a sequence of “two crossing ribbons”, without closing the ends as in the initial “8” knot.
The three arrays all together compose the pattern I was looking for, made of the two simple basic sketch objects.
It is still a 2D drawing, the 3D alternate overlapping of the two threads is left to the imagination of the observer, while it could be helped with colors.
As a fan of the works of a geometry genius as M.C.Escher, I also started trying to imagine how this shape could be turned and placed in 2D space to auto intersect with its own copies… see my next post.