5 ms·

Celtic Code: Drawing knots with Python

82 points by HansardExpert 11mo ago

HansardExpert 11mo ago
A web app that uses Python to create Celtic knots and it's really fun!
- xnx 10mo ago
  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)) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ MemoryError
  - 2earth 10mo ago
    200x200? You're crazy! Also: yes, good idea
hodgehog11 10mo ago
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 https://www.nature.com/articles/s41586-021-04086-x for example.
velcrovan 10mo 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 https://archive.org/details/celticknotwork0000bain/mode/2up
- quag 10mo ago
  Thank you! I’ll have to take a look.
- gilleain 10mo ago
  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.
  - gilleain 10mo ago
    Actually, this is described well in reverse here : https://armory-rasa.tumblr.com/post/151872673763/drawing-with-gremble-reverse-engineering-celtic https://armory-rasa.tumblr.com/post/151872673763/drawing-wit...
- mcphage 10mo ago
  So I do agree with you that Iain Bain's methods is better than his father's, especially for us mere mortals. But George's method for consistent rope widths (step 1: draw them all the same width) did work better for me when I was getting a program to generate knotwork on grid of squares and rhombuses, where following Iain's method led to irregular rope widths because the angles changed.
iansteyn 10mo ago
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!!
iansteyn 10mo ago
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?
- jonahx 10mo ago
  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.
  - marssaxman 10mo ago
    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.
- NoboruWataya 10mo ago
  Is "procedural generation" not exactly that? I wouldn't think of genAI when I hear that term.
  - iansteyn 10mo ago
    Yeah fair enough. I don’t think of genAI either when I hear “procedural generation” (or CGI - “Computer Generated Imagery” - for that matter). But the word “generate” has taken on new significance for the broader public now and I’m not sure that non-technical folks know the difference.
- 10mo ago
OscarCunningham 10mo ago
Fans of Celtic knots might also like the daily game Celtix (https://www.andrewt.net/puzzles/celtix/ https://www.andrewt.net/puzzles/celtix/) where the objective is to separate a Celtic knot into five coloured strands.
cyrusradfar 10mo ago
Dropping a thank you to the OP for sharing. Really enjoyed how you traced your mental model through the journey of solving the problem.
foofoo12 10mo ago
Webapp doesn't work for me (current version Firefox): Uncaught TypeError: loading.showModal is not a function <anonymous> https://2earth.pyscriptapps.com/celtic-knot/ latest/:20 latest:20:17 <anonymous> https://2earth.pyscriptapps.com/celtic-knot/ latest/:20 and Uncaught (in promise) DOMException: IDBFactory.open: The operation is insecure <anonymous> index.js:65 Xe index.js:63 Ye sync.js:8 engine pyodide.js:95 get interpreters.js:36 promise callback*get/< interpreters.js:34 xn loader.js:66 promise callback*xn loader.js:66 Kn script-handler.js:91 or custom.js:99 define custom.js:266 <anonymous> core.js:307 promise callback\* core.js:182 core-Dwn9Kajy.js:1
- 2earth 10mo ago
  Thanks, I'll look into it
taeric 10mo ago
If you are interested in this art style, Knuth shared that there is a very cool art display that includes Celtic Tours. https://www-cs-faculty.stanford.edu/~knuth/knights.html https://www-cs-faculty.stanford.edu/~knuth/knights.html is his writeup on the art. If you are in the area, highly recommend getting to see it.
imba404 10mo ago
You should check out Knot dice, which is a fun tactile way to make one. www.blackoakgames.com/collections/knot-dice

82 points by HansardExpert 11mo ago

HansardExpert 11mo ago

A web app that uses Python to create Celtic knots and it's really fun!

xnx 10mo ago
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)) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ MemoryError
- 2earth 10mo ago
  200x200? You're crazy! Also: yes, good idea

hodgehog11 10mo ago

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 https://www.nature.com/articles/s41586-021-04086-x for example.

velcrovan 10mo 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 https://archive.org/details/celticknotwork0000bain/mode/2up

quag 10mo ago
Thank you! I’ll have to take a look.
gilleain 10mo ago
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.
- gilleain 10mo ago
  Actually, this is described well in reverse here : https://armory-rasa.tumblr.com/post/151872673763/drawing-with-gremble-reverse-engineering-celtic https://armory-rasa.tumblr.com/post/151872673763/drawing-wit...
mcphage 10mo ago
So I do agree with you that Iain Bain's methods is better than his father's, especially for us mere mortals. But George's method for consistent rope widths (step 1: draw them all the same width) did work better for me when I was getting a program to generate knotwork on grid of squares and rhombuses, where following Iain's method led to irregular rope widths because the angles changed.

iansteyn 10mo ago

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!!

iansteyn 10mo ago

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?

jonahx 10mo ago
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.
- marssaxman 10mo ago
  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.
NoboruWataya 10mo ago
Is "procedural generation" not exactly that? I wouldn't think of genAI when I hear that term.
- iansteyn 10mo ago
  Yeah fair enough. I don’t think of genAI either when I hear “procedural generation” (or CGI - “Computer Generated Imagery” - for that matter). But the word “generate” has taken on new significance for the broader public now and I’m not sure that non-technical folks know the difference.
10mo ago

OscarCunningham 10mo ago

Fans of Celtic knots might also like the daily game Celtix (https://www.andrewt.net/puzzles/celtix/ https://www.andrewt.net/puzzles/celtix/) where the objective is to separate a Celtic knot into five coloured strands.

cyrusradfar 10mo ago

Dropping a thank you to the OP for sharing. Really enjoyed how you traced your mental model through the journey of solving the problem.

foofoo12 10mo ago

Webapp doesn't work for me (current version Firefox): Uncaught TypeError: loading.showModal is not a function <anonymous> https://2earth.pyscriptapps.com/celtic-knot/ latest/:20 latest:20:17 <anonymous> https://2earth.pyscriptapps.com/celtic-knot/ latest/:20 and Uncaught (in promise) DOMException: IDBFactory.open: The operation is insecure <anonymous> index.js:65 Xe index.js:63 Ye sync.js:8 engine pyodide.js:95 get interpreters.js:36 promise callback*get/< interpreters.js:34 xn loader.js:66 promise callback*xn loader.js:66 Kn script-handler.js:91 or custom.js:99 define custom.js:266 <anonymous> core.js:307 promise callback\* core.js:182 core-Dwn9Kajy.js:1

2earth 10mo ago
Thanks, I'll look into it

taeric 10mo ago

If you are interested in this art style, Knuth shared that there is a very cool art display that includes Celtic Tours. https://www-cs-faculty.stanford.edu/~knuth/knights.html https://www-cs-faculty.stanford.edu/~knuth/knights.html is his writeup on the art. If you are in the area, highly recommend getting to see it.

imba404 10mo ago

You should check out Knot dice, which is a fun tactile way to make one. www.blackoakgames.com/collections/knot-dice