The first geometrical challenge puzzling my mind was how to combine together two ore more knot patterns, oriented at special angles one respect to the other, making it look like a continuous pattern, with no weird crossings or overlaps. As my first pattern had all crossovers at 45 deg, I thought the feasible choice would be to link two patterns at a right angle. The diagonal parts were already properly oriented, but it has been a little bit tricky to find the right distance between the two patterns to preserve the regularity of cross overs. After a few attempts I realised the obvious: they should have been placed at 90 deg one respect to the other, each pattern starting at the same coordinate of the side of the other, leaving a free square where they would intersect if extended, the side of which corresponds to the width of each thread.

The next step is to design the angular connecting block, joining the threads of both patterns, in way that geometrically could represent a 3D physically possible continuity (my goal is to create 3D printable objects, not 2D “impossible” paintings). To be noticed that the angular block must match the geometry of the crossovers and the width of the threads: threads with longer or shorter elements, of the same width can use the same angular block.

As an alternative, the horizontal thread can be moved up an left, to match it’s upper left diagonal side with the lower right diagonal side of the vertical thread, shrinking the angular part as in the picture. This is more compact but optically more tricky to imagine the vertical ribbon bending with a 45 deg angle and such a spiky external corner. It could be easier imagined as sheet of paper either folded as an origami or with the shapes cutout and then interwoven by hand.

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