Tree of Knots, Knotty Fractal, Carpenter's Lock

Tree of Knots, Knotty Fractal

I have used the carpenter’s lock (aka. cross or knot) with hundreds of children and adults. It is one of the simplest models to start a conversation about 3D, something they can take home and show to adults. I have observed children trying to connect the pieces in all sorts of structures, some of which are fairly long. So, I decided to make some dual-pieces for more building opportunities.

Given three pieces, say, A, B, C, there are six ways to combine them—{AA, BB, CC, AB, AC, BC}. Therefore we have six dual-pieces in a set. Indeed, we do not need all the six pieces to build a growing three. For example, the subset {AB, AC, BC} is adequate.
Please start with a set of medium or loose connections and test them on your printer. A resolution of 0.2mm works well for me.

To Build a Tree of Knots

Just follow the basic knotty structure (shown in the figures) and allow it to grow in all directions. Wherever you do not want to continue, please try a simple knot.

Among the Files

1. Three sets of six dual pieces at three levels of tolerance.
2. Three sets of single pieces at three levels of tolerance for endpoints.
3. Six single dual-pieces that are loose.

Questions to Explore

1. As the tree of knots grows, how many pieces are there in the tree?
2. How much time does it take to undo the knots in a certain tree?