Celtic Code: Drawing Knots with Python
2earth.github.io67 points by HansardExpert 14 days ago
67 points by HansardExpert 14 days ago
The linked article references George Bain’s book on Celtic knotwork construction methods, but his son Ian Bain actually found a much, much better method, and argues convincingly that this, not his father’s, was the method used by medieval Celtic illustrators. Ian’s method more easily produces consistent rope widths (when done by hand), and addresses the issue of how to soften these angular turns which ruin the rope effect and produce a robotic grid.
The book is out of print now but it looks like you can borrow it on archive.org: https://archive.org/details/celticknotwork0000bain/mode/2up
Interested in what Iain's method might be, but the method I like is:
1) Draw the 'skeleton' as a connected (simple?) graph in the plane
2) Place crosses at the midpoint of each edge
3) Connect the crosses with shortest (non-crossing!) connections (bit vague this, but is more obvious by hand)
4) Erase the crosses, and run over the line, assigning under/over as appropriate - you can also thicken at this step
This gives good free-standing knots, although may be more work for the dense knotwork in the OP's examples.
Actually, this is described well in reverse here :
https://armory-rasa.tumblr.com/post/151872673763/drawing-wit...
This post makes me wonder - does anyone else think there is a need for a term to more strongly differentiate between procedural generation (like this knot-drawing program) and genAI? I feel it really diminishes the impact of the work of programmer-artists nowadays to say they make “computer-generated” art. Or maybe we already have such a term?
I instinctively agree there is an important difference.
If you try to define systematically what that difference is, though, it's not obvious. At the end of day, I think it's something like "degree of difficulty" or "amount of thought", which are vague concepts. Yet most would agree what the author here did requires more skill and thinking than typing "image of celtic knot" into Gemini.
I used to work on procedural graphics, and to me the clear difference is that all the training involved happened inside my brain. This author's article describes a similar process. He's not throwing a lot of existing examples into a black box, letting it learn their features, then driving it to emit new images with similar features: he is learning, himself, what those features are, inventing a process which fits those bounds, then automating it with code.
Is "procedural generation" not exactly that? I wouldn't think of genAI when I hear that term.
Fans of Celtic knots might also like the daily game Celtix (https://www.andrewt.net/puzzles/celtix/) where the objective is to separate a Celtic knot into five coloured strands.
I'm thinking this might have broader use than artistic appeal. From what I've heard, knot generation is a young but increasingly important topic in knot theory, since it can be used to generate data to train ML models on, and subsequently (hopefully) discover new algorithms for knot classification. See https://www.nature.com/articles/s41586-021-04086-x for example.
I really like how the author walks us through the generation process step-by-step. It makes it seem possible for me to build stuff like this too!!
A web app that uses Python to create Celtic knots and it's really fun!
Looks neat. Might be worth constraining the inputs. I got an error at 200x200:
Uncaught PythonError: Traceback (most recent call last):
File "<exec>", line 22, in resetKnot
File "<exec>", line 473, in generateKnot
File "/lib/python3.12/site-packages/PIL/Image.py", line 2941, in new
return im._new(core.fill(mode, size, color))
^^^^^^^^^^^^^^^^^^^^^^^^^^^^