4 ms·

Rafael Araujo's 20 Mesmerizing Geometrical Masterpieces (2024)

126 points by NoRagrets 2y ago

deleted 2y ago
[deleted]
monkmartinez 2y ago
At first glance the "masterpieces" looked like a crap ton of lines and circles around a sketched shell or butterfly. You know, the kind you see when you tell Stable Diffusion to "sketch". Then I watched the video for a sec... WOAH!!! He is talking about a "formula" quite a bit... ctrl-f "formula" == 0 results. Google: Rafael Araujo artist formula. Ahhhh! https://www.rafael-araujo.com/calculation https://www.rafael-araujo.com/calculation Now we are getting somewhere... and another that shows the process a bit better: https://hazelhomeartandantiques.blogspot.com/2015/04/the-calculations-of-rafael-araujo-b-1957.html https://hazelhomeartandantiques.blogspot.com/2015/04/the-cal... Now I am trawling github to see if I can find some processing or similar libraries that I can play around with. Golden Ratio sketches, defining physical objects and shapes from purely mathematical constructions... I love rabbit holes!
- nequals30 2y ago
  Inigo Quilez has some good videos generating art and scenes with just mathematical constructions: https://www.youtube.com/c/InigoQuilez https://www.youtube.com/c/InigoQuilez
- sixtyj 2y ago
  This is a deep rabbit hole indeed :) Does Donald Knuth have any metaprogramming for golden section/ratio? About golden section in the universe there is a nice book by Scott Olsen - https://www.goodreads.com/book/show/316282.The_Golden_Section https://www.goodreads.com/book/show/316282.The_Golden_Sectio...
- openrisk 2y ago
  Would be very pleasantly surprised if a drawing like "Blue Spikes Shell" is actually reducible to a readable mathematical construction. A surface that exhibits very strong variability in curvature (like the spikes in the shell) is most likely a collage of different pieces. These would (at best) have only a locally valid mathematical formula. Achieving a visually convincing result through smooth patching introduces lots of ugly "numbers". Most likely the "formula" concerns only some aspects of the drawing, like overall symmetry and relative sizes.
gilleain 2y ago
Technically amazing - such fine detail, and of course precision. However ... I recently heard the saying "a great artist knows when to stop" (it was Ben Afflek talking about AI art - I guess he was quoting someone?). I feel like in the case of these drawings, less detail would actually be better. More readable, perhaps. Still, an impressive amount of effort for each one, given only straightedge and compass.
- BLKNSLVR 2y ago
  I think the detail IS the art, or at least the strongest element that the artist wishes to demonstrate. Removing the details removes the reference to the formula(e), which is the soul around which the beatiful pictures are created. In this case, the art is the process, more-so than the end result - which is a by-product.
Mistletoe 2y ago
Is the Monarch one based on a geometric way they fly or something?
- victor22 2y ago
  [flagged]
Yestas 2y ago
I believe that we still know so little about nature and its laws. Sometimes it seems that we are moving in the direction of technological development instead of developing our knowledge about nature and aligning ourselves with it.
- dcreater 2y ago
  Hi, id like to introduce you to eastern philosophy
dymax78 2y ago
~10 years ago I had a renewed interested in perspective drawing, and was struggling with an 'exercise' that utilized curvilinear perspective & oblique angles. Anyways, I stumbled on some of Rafael's drawings and found their inclusion of the guide lines / measuring lines invaluable, but for the hell of it, I emailed him some questions. He promptly responded and then dumped images and reference material on dropbox for me - very nice guy. Personal fav is "Dürer" that demonstrates Albrecht Dürers method of projecting a spiral. https://www.rafael-araujo.com/product-page/d%C3%BCrer# https://www.rafael-araujo.com/product-page/d%C3%BCrer#
mkl 2y ago
> he unfolds the significance of the Golden Ratio, showcasing its spiritual depth and presence within the natural order. Yikes. The golden ratio has limited significance, nothing to do with spirituality, and little presence in nature [1]. Araujo's pictures look great, but in almost any of them you could replace the golden ratio with 1.6, 1.7, or 1.5, and get something no less beautiful. The Wikipedia page is fairly good on this, especially the "Disputed observations" section: https://en.wikipedia.org/wiki/Golden_ratio#Disputed_observations https://en.wikipedia.org/wiki/Golden_ratio#Disputed_observat... As a mathematician, fetishisation of the golden ratio bugs me. [1] The main place is spiral arrangements of leaves, petals, etc. Vi Hart explains why (watch all three parts): https://www.youtube.com/watch?v=ahXIMUkSXX0 https://www.youtube.com/watch?v=ahXIMUkSXX0
- deleted 2y ago
  [deleted]
- numpy-thagoras 2y ago
  > As a mathematician, fetishisation of the golden ratio bugs me. I know, but hear me out: it's a decent hook for teaching people about Geometry, Recursion, and Dynamic Programming.
- esperent 2y ago
  I'm also a mathematician, and it doesn't bug me at all. > nothing to do with spirituality It clearly does have a lot to do with spirituality, for many people, as symbol. Much as the cross does for Christans. Neither of these symbols have spiritual meaning to me - a cross is just a cross, a spiral is just a spiral. I don't have much need for spiritual symbolism myself - when I meditate, I rather to focus on a simple sound or light source - but I'd consider it highly egotistical of myself if I was to start judging other people's use of symbols just because they don't understand maths, or whatever. > fetishisation I've yet to ever see this word used except to denigrate other people's beliefs, or as an attempt to make the user feel superior. I believe you did both here. My advice, one mathematician to another: chill and let people have their symbols. Don't expect them to have a deep understanding of mathematics, much as we don't have a deep understanding of their need for spiritual symbolism. Nonetheless we can let each other be, and all get along. Who knows, perhaps a fascination with this "sacred geometry" as they call it, might be a starting point for someone to have a genuine interest in mathematics.
tzury 2y ago
https://x.com/rafaela31416 https://x.com/rafaela31416
world2vec 2y ago
I own a framed print of the first one (the orange butterflies) and it's a delight.

126 points by NoRagrets 2y ago

deleted 2y ago

[deleted]

At first glance the "masterpieces" looked like a crap ton of lines and circles around a sketched shell or butterfly. You know, the kind you see when you tell Stable Diffusion to "sketch". Then I watched the video for a sec... WOAH!!! He is talking about a "formula" quite a bit... ctrl-f "formula" == 0 results. Google: Rafael Araujo artist formula. Ahhhh! https://www.rafael-araujo.com/calculation https://www.rafael-araujo.com/calculation Now we are getting somewhere... and another that shows the process a bit better: https://hazelhomeartandantiques.blogspot.com/2015/04/the-calculations-of-rafael-araujo-b-1957.html https://hazelhomeartandantiques.blogspot.com/2015/04/the-cal... Now I am trawling github to see if I can find some processing or similar libraries that I can play around with. Golden Ratio sketches, defining physical objects and shapes from purely mathematical constructions... I love rabbit holes!

nequals30 2y ago
Inigo Quilez has some good videos generating art and scenes with just mathematical constructions: https://www.youtube.com/c/InigoQuilez https://www.youtube.com/c/InigoQuilez
sixtyj 2y ago
This is a deep rabbit hole indeed :) Does Donald Knuth have any metaprogramming for golden section/ratio? About golden section in the universe there is a nice book by Scott Olsen - https://www.goodreads.com/book/show/316282.The_Golden_Section https://www.goodreads.com/book/show/316282.The_Golden_Sectio...
openrisk 2y ago
Would be very pleasantly surprised if a drawing like "Blue Spikes Shell" is actually reducible to a readable mathematical construction. A surface that exhibits very strong variability in curvature (like the spikes in the shell) is most likely a collage of different pieces. These would (at best) have only a locally valid mathematical formula. Achieving a visually convincing result through smooth patching introduces lots of ugly "numbers". Most likely the "formula" concerns only some aspects of the drawing, like overall symmetry and relative sizes.

gilleain 2y ago

Technically amazing - such fine detail, and of course precision. However ... I recently heard the saying "a great artist knows when to stop" (it was Ben Afflek talking about AI art - I guess he was quoting someone?). I feel like in the case of these drawings, less detail would actually be better. More readable, perhaps. Still, an impressive amount of effort for each one, given only straightedge and compass.

BLKNSLVR 2y ago
I think the detail IS the art, or at least the strongest element that the artist wishes to demonstrate. Removing the details removes the reference to the formula(e), which is the soul around which the beatiful pictures are created. In this case, the art is the process, more-so than the end result - which is a by-product.

Mistletoe 2y ago

Is the Monarch one based on a geometric way they fly or something?

victor22 2y ago
[flagged]

Yestas 2y ago

I believe that we still know so little about nature and its laws. Sometimes it seems that we are moving in the direction of technological development instead of developing our knowledge about nature and aligning ourselves with it.

dcreater 2y ago
Hi, id like to introduce you to eastern philosophy

dymax78 2y ago

~10 years ago I had a renewed interested in perspective drawing, and was struggling with an 'exercise' that utilized curvilinear perspective & oblique angles. Anyways, I stumbled on some of Rafael's drawings and found their inclusion of the guide lines / measuring lines invaluable, but for the hell of it, I emailed him some questions. He promptly responded and then dumped images and reference material on dropbox for me - very nice guy. Personal fav is "Dürer" that demonstrates Albrecht Dürers method of projecting a spiral. https://www.rafael-araujo.com/product-page/d%C3%BCrer# https://www.rafael-araujo.com/product-page/d%C3%BCrer#

mkl 2y ago

> he unfolds the significance of the Golden Ratio, showcasing its spiritual depth and presence within the natural order. Yikes. The golden ratio has limited significance, nothing to do with spirituality, and little presence in nature [1]. Araujo's pictures look great, but in almost any of them you could replace the golden ratio with 1.6, 1.7, or 1.5, and get something no less beautiful. The Wikipedia page is fairly good on this, especially the "Disputed observations" section: https://en.wikipedia.org/wiki/Golden_ratio#Disputed_observations https://en.wikipedia.org/wiki/Golden_ratio#Disputed_observat... As a mathematician, fetishisation of the golden ratio bugs me. [1] The main place is spiral arrangements of leaves, petals, etc. Vi Hart explains why (watch all three parts): https://www.youtube.com/watch?v=ahXIMUkSXX0 https://www.youtube.com/watch?v=ahXIMUkSXX0

deleted 2y ago
[deleted]
numpy-thagoras 2y ago
> As a mathematician, fetishisation of the golden ratio bugs me. I know, but hear me out: it's a decent hook for teaching people about Geometry, Recursion, and Dynamic Programming.
esperent 2y ago
I'm also a mathematician, and it doesn't bug me at all. > nothing to do with spirituality It clearly does have a lot to do with spirituality, for many people, as symbol. Much as the cross does for Christans. Neither of these symbols have spiritual meaning to me - a cross is just a cross, a spiral is just a spiral. I don't have much need for spiritual symbolism myself - when I meditate, I rather to focus on a simple sound or light source - but I'd consider it highly egotistical of myself if I was to start judging other people's use of symbols just because they don't understand maths, or whatever. > fetishisation I've yet to ever see this word used except to denigrate other people's beliefs, or as an attempt to make the user feel superior. I believe you did both here. My advice, one mathematician to another: chill and let people have their symbols. Don't expect them to have a deep understanding of mathematics, much as we don't have a deep understanding of their need for spiritual symbolism. Nonetheless we can let each other be, and all get along. Who knows, perhaps a fascination with this "sacred geometry" as they call it, might be a starting point for someone to have a genuine interest in mathematics.

tzury 2y ago

https://x.com/rafaela31416 https://x.com/rafaela31416

world2vec 2y ago

I own a framed print of the first one (the orange butterflies) and it's a delight.