# Tree of Knots, Knotty Fractal, Carpenter's Lock

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## 3D model description

####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?

• 3D file format: STL

## Creator

STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU