Intriguing Tessellations
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Intriguing Tessellations
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Re: Intriguing Tessellations
#2Where did you ever find this? I knew those roses would tie in somehow.
Re: Intriguing Tessellations
#3A bit of context: Marjorie Rice achieved minor fame for discovering a number of new ways that (irregular) pentagons can tile the plane -- a surprising feat for an amateur mathematician. You can read more about her on here https://www.quantamagazine.org/marjorie-rices-secret-pentago... and more about pentagonal tessellations here https://en.wikipedia.org/wiki/Pentagonal_tiling, along with a history for when the different tessellations were discovered over the past century or so.
Personally, I love this webpage partially because it's just so different than what I'm used to for the pages of mathematicians. It really comes across as made by someone who was extremely talented at math but who only saw it only as a pastime and never bothered to integrate into the mathematical community.
Re: Intriguing Tessellations
#4A bit of context: Marjorie Rice achieved minor fame for discovering a number of new ways that (irregular) pentagons can tile the plane -- a surprising feat for an amateur mathematician. You can read more about her on here https://www.quantamagazine.org/marjorie-rices-secret-pentago... and more about pentagonal tessellations here https://en.wikipedia.org/wiki/Pentagonal_tiling , along with a history for when the diffe…
LOL I opened this thread just to post a link to the Quanta magazine site. It's a very well done article and applies a great human element to the story. Dementia is one of the few things that scares me.
For an amateur mathematician to do this is, as you say, a surprising feat. I'd go beyond that to add a bunch more superlatives.
It is stories like her story that serve as good reminders that the idea of citizen scientists is healthy and should be encouraged.
I highly recommend the link you provided. It's a bit long but well written.
And another that I just found and read:
https://www.conquermaths.com/news/post/index/264/Marjorie-Ri...
Re: Intriguing Tessellations
#5A recent computer-aided proof found the last remaining pentagon tesselations.
Re: Intriguing Tessellations
#6I occasionally design fabric patterns, so the pages on applying graphics to the tessellations are interesting to me. What I'd like to end up with is a generalised script for creating repeating patterns from a small set of images (e.g. dinosaur outlines for kids' clothing, or flowers for haberdashery). If I could be procedurally generating a variety of designs based on different tessellations, it would greatly increase my potential output.
Re: Intriguing Tessellations
#7I occasionally design fabric patterns, so the pages on applying graphics to the tessellations are interesting to me. What I'd like to end up with is a generalised script for creating repeating patterns from a small set of images (e.g. dinosaur outlines for kids' clothing, or flowers for haberdashery). If I could be procedurally generating a variety of designs based on different tessellations, it would greatly increas…
This doesn't quite answer the question that you're asking, but there's a semi-old research paper that seems related to what you want: http://www.cgl.uwaterloo.ca/csk/projects/escherization/ No readily-usable scripts that I'm aware of unfortunately.
Re: Intriguing Tessellations
#8I occasionally design fabric patterns, so the pages on applying graphics to the tessellations are interesting to me. What I'd like to end up with is a generalised script for creating repeating patterns from a small set of images (e.g. dinosaur outlines for kids' clothing, or flowers for haberdashery). If I could be procedurally generating a variety of designs based on different tessellations, it would greatly increas…
This doesn't quite answer the question that you're asking, but there's a semi-old research paper that seems related to what you want: http://www.cgl.uwaterloo.ca/csk/projects/escherization/ No readily-usable scripts that I'm aware of unfortunately.
That is an interesting read, thank you. You might also describe what I'm doing as trying to efficiently pack a polygon with non-overlapping images, then tessellating that polygon as a method of repetition. Easy to conceive with squares or triangles, but the pentagons in OP's link would produce more organic patterns in my opinion.
Re: Intriguing Tessellations
#9A bit of context: Marjorie Rice achieved minor fame for discovering a number of new ways that (irregular) pentagons can tile the plane -- a surprising feat for an amateur mathematician. You can read more about her on here https://www.quantamagazine.org/marjorie-rices-secret-pentago... and more about pentagonal tessellations here https://en.wikipedia.org/wiki/Pentagonal_tiling , along with a history for when the diffe…
It's really nice. It makes me think she would have been a great person to know and be around.
Re: Intriguing Tessellations
#10Earlier quoted context omitted.
This doesn't quite answer the question that you're asking, but there's a semi-old research paper that seems related to what you want: http://www.cgl.uwaterloo.ca/csk/projects/escherization/ No readily-usable scripts that I'm aware of unfortunately.
That is an interesting read, thank you. You might also describe what I'm doing as trying to efficiently pack a polygon with non-overlapping images, then tessellating that polygon as a method of repetition. Easy to conceive with squares or triangles, but the pentagons in OP's link would produce more organic patterns in my opinion.
Ahh, neat! That sounds like it results in some nice patterns. In that case, this paper might be more relevant http://www.cse.cuhk.edu.hk/~ttwong/papers/pad/pad.html. Its related work section should also have some good references to other things like this. For the most part they'll likely be too complex to make them worth implementing, but it might still be interesting or give you some inspiration for new ideas.