[math-fun] Fibonacci/Golden Ratio in Art
A friend of mine who works in an art museum is looking at Fibonacci influences in art. Yes, this has been done many, many times before, and I've seen a number of exhibitions of this type, but I haven't been that impressed by the artistic and mathematical quality or depth of insight provided by most of these previous exhibitions. Furthermore, many (if not most) of the supposed findings of phi (the Golden ratio) in art are spurious coincidences, without any shred of evidence that the artist knew anything about golden ratios. A big problem is finding images/sculptures/animations that are both interesting/fun to look at, but also provide interesting/fun mathematical/geometric insights. I'm hoping that some of you have been equally disappointed in previous exhibitions of this type, and may have some "pet" images/ideas/insights that you'd like to see in such an exhibition. This may be your chance to get artistic attribution! He has not allowed me to go public with his name or museum affiliation, so I can't tell you those things yet -- it may be a number of months. But you may want to be on the lookout for interesting ideas to put into the back of your mind. Some obvious things: Penrose tilings, Archimedes spiral gears, flowers, sea shells, etc. But I'd love to see some 3D-printed sculptures of cool shapes. Animations of mechanisms would also be very cool. I'd love to find any Islamic geometric art that utilizes phi. -------- While Google searching for Fibonacci/phi, I asked myself about the phi number field. Anything interesting there?
While Google searching for Fibonacci/phi, I asked myself about the phi number field. Anything interesting there?
Every regular n-polytope (where n >= 3) is geometrically similar to a finite subset of the vector space F^(n+1), where F is the field of characteristic zero generated by phi. Best wishes, Adam P. Goucher
Hi Henry, I have THE golden ratio nautilus. (The only one.) See: https://www.youtube.com/watch?v=_gxC8OjoQkQ Unfortunately many people in the art world, loooking for math connections they can understand and explain to others, repeat all kinds of published nonsense about the golden ratio in art. I made an anti-propaganda video that I send to such people: https://www.simonsfoundation.org/2015/03/27/mathematical-impressions-the-gol... But to the larger question of art that does have mathematical foundations of some sort, there are lots of examples in the galleries of the past Bridges Conference and JMM Art Exhibitions. As with any kind of art, everyone will have their own taste as to what is interesting and what is disappointing, but you can take a look through the examples here and I'd be happy to connect you with any of the artists if you wish: http://gallery.bridgesmathart.org/exhibitions George http://georgehart.com On 4/26/2020 12:33 PM, Henry Baker wrote:
A friend of mine who works in an art museum is looking at Fibonacci influences in art.
Yes, this has been done many, many times before, and I've seen a number of exhibitions of this type, but I haven't been that impressed by the artistic and mathematical quality or depth of insight provided by most of these previous exhibitions.
Furthermore, many (if not most) of the supposed findings of phi (the Golden ratio) in art are spurious coincidences, without any shred of evidence that the artist knew anything about golden ratios.
A big problem is finding images/sculptures/animations that are both interesting/fun to look at, but also provide interesting/fun mathematical/geometric insights.
I'm hoping that some of you have been equally disappointed in previous exhibitions of this type, and may have some "pet" images/ideas/insights that you'd like to see in such an exhibition.
This may be your chance to get artistic attribution!
He has not allowed me to go public with his name or museum affiliation, so I can't tell you those things yet -- it may be a number of months.
But you may want to be on the lookout for interesting ideas to put into the back of your mind.
Some obvious things: Penrose tilings, Archimedes spiral gears, flowers, sea shells, etc. But I'd love to see some 3D-printed sculptures of cool shapes. Animations of mechanisms would also be very cool. I'd love to find any Islamic geometric art that utilizes phi.
-------- While Google searching for Fibonacci/phi, I asked myself about the phi number field. Anything interesting there?
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fibo + artist
... Mario Merz, of course. à+ É. Catapulté de mon aPhone
Le 26 avr. 2020 à 18:33, Henry Baker <hbaker1@pipeline.com> a écrit :
A friend of mine who works in an art museum is looking at Fibonacci influences in art.
Yes, this has been done many, many times before, and I've seen a number of exhibitions of this type, but I haven't been that impressed by the artistic and mathematical quality or depth of insight provided by most of these previous exhibitions.
Furthermore, many (if not most) of the supposed findings of phi (the Golden ratio) in art are spurious coincidences, without any shred of evidence that the artist knew anything about golden ratios.
A big problem is finding images/sculptures/animations that are both interesting/fun to look at, but also provide interesting/fun mathematical/geometric insights.
I'm hoping that some of you have been equally disappointed in previous exhibitions of this type, and may have some "pet" images/ideas/insights that you'd like to see in such an exhibition.
This may be your chance to get artistic attribution!
He has not allowed me to go public with his name or museum affiliation, so I can't tell you those things yet -- it may be a number of months.
But you may want to be on the lookout for interesting ideas to put into the back of your mind.
Some obvious things: Penrose tilings, Archimedes spiral gears, flowers, sea shells, etc. But I'd love to see some 3D-printed sculptures of cool shapes. Animations of mechanisms would also be very cool. I'd love to find any Islamic geometric art that utilizes phi.
-------- While Google searching for Fibonacci/phi, I asked myself about the phi number field. Anything interesting there?
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Does it matter if the artist is aware of the math? Perhaps the question should be why there is an irrational number that approximates a parameter for the human visual system: https://www.theguardian.com/artanddesign/2009/dec/28/golden-ratio-us-academi... But I don't think anything beyond the tenths place matters, visually. Helaman Ferguson's sculptures are the most masterful combinations of art and math that I've seen. Complete awareness. Ruth McDowell created a superb Fibonacci quilt: https://www.internationalquiltmuseum.org/quilt/20080400227 She has many other quilts with mathematical themes. The artistic representation of phi is one of the persistent themes of Gathering for Gardner. I would like to see (hear, taste, feel) more art that represents math, even at the expense of the artistic aesthetic. I'd like to have the balance point shifted towards math. Some artists working early in the twentienth century felt influenced by developments in physics, allegedly. I never understood that in any way other than a feeling of being free to investigate radically new ideas. It would have been more interesting if the physicists had felt free to express their research in art, rather than the other way round.
Furthermore, many (if not most) of the supposed findings of phi (the Golden ratio) in art are spurious coincidences, without any shred of evidence that the artist knew anything about golden ratios.
A big problem is finding images/sculptures/animations that are both interesting/fun to look at, but also provide interesting/fun mathematical/geometric insights.
Hilarie
For example: https://www.zirckelvndrichtscheyt.com/e-n-g-l-i-s-h-1/geometricized-heads/ I think that less is known about the later Wenzel Jamnitzer (and possibly others): https://upload.wikimedia.org/wikipedia/commons/a/ac/Schreibzeug_%28Jamnitzer... https://artsandculture.google.com/asset/jewelry-box-probably-from-the-worksh... (the golden rectangles are not golden rectangles, but the filigree therein looks similar to: https://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jan/... ) Jewelry boxes are a good target for incorporating vanity, or if religion is a better selling point, possibly try looking at Catholic tabernacles. I feel the same about the idea of searching art for golden ratio as I do about searching iNaturalist for population curves of one particular shape. Aspect ratio is an extracted parameter. If your data set is large enough, you will hit 1.6 a few times, maybe enough to get a publication. If the audience is gullible, maybe they will buy the conclusion that golden ratio is important, but this is sleight of hand where *a lot* of other proportions have been ignored... Possibly even a worse bias than ballet, though, probably not. If you want to get to the mathematical truth of what the golden ratio is, I would start with the character table of icosahedral symmetry, and then develop the real space matrix representation. After that, it is interesting to consider the generalization of Penrose's tiling to Danzer ABCK, see also: https://demonstrations.wolfram.com/TransformationOfIcosahedralSolidsInZ15/ Then there is still the problem of "well it's not art". So what? Look what they did at Institute for Advanced study: https://www.ias.edu/idea-tags/concinnitas . IAS is the house of the grand leaders and the trend setters, well in this case, they aren't setting the bar very high. When I made correlated figure 12 and Table IV for the "prelude" to my dissertation, at least I put some color into it! (There is also an Icosidodecahedron in there, V.G.1 page 28 & 29: https://github.com/bradklee/Dissertation/blob/master/Prelude/Prelude.pdf, see also: https://oeis.org/A318495) --Brad
On Apr 26, 2020, at 11:34 AM, Henry Baker <hbaker1@pipeline.com> wrote: Yes, this has been done many, many times before...
On Mon, Apr 27, 2020 at 5:48 AM Brad Klee <bradklee@gmail.com> wrote:
For example: https://www.zirckelvndrichtscheyt.com/e-n-g-l-i-s-h-1/geometricized-heads/
Yes, Albrecht Dürer was very interested in mathematics. See here: https://www.flickr.com/photos/jbuddenh/31131350214 for more history about this. His famous image: Melencolia I, shows (among lots of other things) a polyhedron which appears to be a truncated rhombohedron (some say a truncated cube). See it here: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg James
oops -- somehow I had a link to an Andy Goldsworthy spiral in my previous email. Well it was a nice spiral of white rocks, at least on topic -- mathematics in art. It was supposed to be a link to history of the artist Albrecht Dürer who was quite interested in mathematics. The correct link for that is: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg James On Mon, Apr 27, 2020 at 10:16 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
On Mon, Apr 27, 2020 at 5:48 AM Brad Klee <bradklee@gmail.com> wrote:
For example: https://www.zirckelvndrichtscheyt.com/e-n-g-l-i-s-h-1/geometricized-heads/
Yes, Albrecht Dürer was very interested in mathematics. See here: https://www.flickr.com/photos/jbuddenh/31131350214 for more history about this.
His famous image: Melencolia I, shows (among lots of other things) a polyhedron which appears to be a truncated rhombohedron (some say a truncated cube). See it here: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg
James
double oops!!! Here is the link to history of life of Albrecht Dürer http://mathshistory.st-andrews.ac.uk/Biographies/Durer.html On Mon, Apr 27, 2020 at 10:25 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
oops -- somehow I had a link to an Andy Goldsworthy spiral in my previous email. Well it was a nice spiral of white rocks, at least on topic -- mathematics in art.
It was supposed to be a link to history of the artist Albrecht Dürer who was quite interested in mathematics. The correct link for that is: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg
James
On Mon, Apr 27, 2020 at 10:16 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
On Mon, Apr 27, 2020 at 5:48 AM Brad Klee <bradklee@gmail.com> wrote:
For example: https://www.zirckelvndrichtscheyt.com/e-n-g-l-i-s-h-1/geometricized-heads/
Yes, Albrecht Dürer was very interested in mathematics. See here: https://www.flickr.com/photos/jbuddenh/31131350214 for more history about this.
His famous image: Melencolia I, shows (among lots of other things) a polyhedron which appears to be a truncated rhombohedron (some say a truncated cube). See it here: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg
James
Here's some art I've created relating to the Fibonacci sequence and Phi. "Fibonacci's Ladder": a Julia set wherein the number of components increases in the Fibonacci sequence. http://www.kerrymitchellart.com/gallery13/ladder.html "Signature of Phi": illustrating the signature sequence of Phi. http://www.kerrymitchellart.com/gallery13/sigphi.html "Geometric Love": nested Fibonacci spirals. http://www.kerrymitchellart.com/gallery16/geolove.html "Irrational Exuberance": coloring Gaussian integers by the fractional part after subtracting multiples of Phi. http://www.kerrymitchellart.com/gallery18/irrationalexuberance.html "2-3-5-8-13": a zoom into the Mandelbrot set showing a spiral with increasing numbers of arms. http://www.kerrymitchellart.com/gallery22/235813.html "Inspired": representing Phi with the Stern-Brocot tree. http://www.kerrymitchellart.com/gallery24/inspired.html "Fibonacci Word 1": a piecewise-linear curve based on the Fibonacci word. http://www.kerrymitchellart.com/gallery35/fibonacci-word1.html "Self Portrait in Phi": using the method from "Signature of Phi" to create a self portrait. http://www.kerrymitchellart.com/gallery61/self-portrait-in-phi.html "Differential Signatures 2": illustrates the differences between two signature sequences, one for a number slightly smaller than phi (phi = 1/Phi) and one for a number slightly larger than phi. http://www.kerrymitchellart.com/gallery90/differential-signatures2.html On Mon, Apr 27, 2020 at 8:27 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
double oops!!!
Here is the link to history of life of Albrecht Dürer
http://mathshistory.st-andrews.ac.uk/Biographies/Durer.html
On Mon, Apr 27, 2020 at 10:25 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
oops -- somehow I had a link to an Andy Goldsworthy spiral in my previous email. Well it was a nice spiral of white rocks, at least on topic -- mathematics in art.
It was supposed to be a link to history of the artist Albrecht Dürer who was quite interested in mathematics. The correct link for that is: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg
James
On Mon, Apr 27, 2020 at 10:16 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
On Mon, Apr 27, 2020 at 5:48 AM Brad Klee <bradklee@gmail.com> wrote:
For example:
https://www.zirckelvndrichtscheyt.com/e-n-g-l-i-s-h-1/geometricized-heads/
Yes, Albrecht Dürer was very interested in mathematics. See here: https://www.flickr.com/photos/jbuddenh/31131350214 for more history about this.
His famous image: Melencolia I, shows (among lots of other things) a polyhedron which appears to be a truncated rhombohedron (some say a truncated cube). See it here: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg
James
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Such wonderful creations! Hilarie
Kerry Mitchell <lkmitch@gmail.com> Here's some art I've created relating to the Fibonacci sequence and Phi.
"Fibonacci's Ladder": a Julia set wherein the number of components increases in the Fibonacci sequence. http://www.kerrymitchellart.com/gallery13/ladder.html
"Signature of Phi": illustrating the signature sequence of Phi. http://www.kerrymitchellart.com/gallery13/sigphi.html
"Geometric Love": nested Fibonacci spirals. http://www.kerrymitchellart.com/gallery16/geolove.html
"Irrational Exuberance": coloring Gaussian integers by the fractional part after subtracting multiples of Phi. http://www.kerrymitchellart.com/gallery18/irrationalexuberance.html
"2-3-5-8-13": a zoom into the Mandelbrot set showing a spiral with increasing numbers of arms. http://www.kerrymitchellart.com/gallery22/235813.html
"Inspired": representing Phi with the Stern-Brocot tree. http://www.kerrymitchellart.com/gallery24/inspired.html
"Fibonacci Word 1": a piecewise-linear curve based on the Fibonacci word. http://www.kerrymitchellart.com/gallery35/fibonacci-word1.html
"Self Portrait in Phi": using the method from "Signature of Phi" to create a self portrait. http://www.kerrymitchellart.com/gallery61/self-portrait-in-phi.html
"Differential Signatures 2": illustrates the differences between two signature sequences, one for a number slightly smaller than phi (phi = 1/Phi) and one for a number slightly larger than phi. http://www.kerrymitchellart.com/gallery90/differential-signatures2.html
Yes, inspiring to hear about an artist willing to go to such great lengths in search of mathematical truth. The other thing to mention is his work on "schneckenlinie". --Brad On Mon, Apr 27, 2020 at 10:27 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
double oops!!!
Here is the link to history of life of Albrecht Dürer
http://mathshistory.st-andrews.ac.uk/Biographies/Durer.html
On Mon, Apr 27, 2020 at 10:25 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
oops -- somehow I had a link to an Andy Goldsworthy spiral in my previous email. Well it was a nice spiral of white rocks, at least on topic -- mathematics in art.
It was supposed to be a link to history of the artist Albrecht Dürer who was quite interested in mathematics. The correct link for that is: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg
James
On Mon, Apr 27, 2020 at 10:16 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
On Mon, Apr 27, 2020 at 5:48 AM Brad Klee <bradklee@gmail.com> wrote:
For example:
https://www.zirckelvndrichtscheyt.com/e-n-g-l-i-s-h-1/geometricized-heads/
Yes, Albrecht Dürer was very interested in mathematics. See here: https://www.flickr.com/photos/jbuddenh/31131350214 for more history about this.
His famous image: Melencolia I, shows (among lots of other things) a polyhedron which appears to be a truncated rhombohedron (some say a truncated cube). See it here: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg
James
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Ah, yes, as here: http://www.mathe.tu-freiberg.de/~hebisch/cafe/duerer/kuenstlerisch.html Especially, since the "golden spiral" is surely math and art, see: https://en.wikipedia.org/wiki/Golden_spiral James On Mon, Apr 27, 2020 at 12:39 PM Brad Klee <bradklee@gmail.com> wrote:
Yes, inspiring to hear about an artist willing to go to such great lengths in search of mathematical truth. The other thing to mention is his work on "schneckenlinie". --Brad
On Mon, Apr 27, 2020 at 10:27 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
double oops!!!
Here is the link to history of life of Albrecht Dürer
http://mathshistory.st-andrews.ac.uk/Biographies/Durer.html
On Mon, Apr 27, 2020 at 10:25 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
oops -- somehow I had a link to an Andy Goldsworthy spiral in my previous email. Well it was a nice spiral of white rocks, at least on topic -- mathematics in art.
It was supposed to be a link to history of the artist Albrecht Dürer who was quite interested in mathematics. The correct link for that is: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg
James
On Mon, Apr 27, 2020 at 10:16 AM James Buddenhagen <jbuddenh@gmail.com
wrote:
On Mon, Apr 27, 2020 at 5:48 AM Brad Klee <bradklee@gmail.com> wrote:
For example:
https://www.zirckelvndrichtscheyt.com/e-n-g-l-i-s-h-1/geometricized-heads/
Yes, Albrecht Dürer was very interested in mathematics. See here: https://www.flickr.com/photos/jbuddenh/31131350214 for more history about this.
His famous image: Melencolia I, shows (among lots of other things) a polyhedron which appears to be a truncated rhombohedron (some say a truncated cube).
See
it here: https://live.staticflickr.com/65535/49825435268_652f6d12a3_b.jpg
James
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I conformally transformed Duerer’s “Melencolia I” so it fits my Phi x 1 laptop screen. Send me an email if you want a copy. -Veit
On Apr 27, 2020, at 4:28 PM, James Buddenhagen <jbuddenh@gmail.com> wrote:
Ah, yes, as here: http://www.mathe.tu-freiberg.de/~hebisch/cafe/duerer/kuenstlerisch.html Especially, since the "golden spiral" is surely math and art, see: https://en.wikipedia.org/wiki/Golden_spiral James
Or if yr tired of the eurocentrism, how about: https://m.youtube.com/watch?v=siFBqH-LaQQ https://m.youtube.com/watch?v=mOMLRMfIYf0 —Brad
On Apr 27, 2020, at 5:54 AM, Brad Klee <bradklee@gmail.com> wrote:
For example: https://www.zirckelvndrichtscheyt.com/e-n-g-l-i-s-h-1/geometricized-heads/
I think that less is known about the later Wenzel Jamnitzer (and possibly others):
https://upload.wikimedia.org/wikipedia/commons/a/ac/Schreibzeug_%28Jamnitzer... https://artsandculture.google.com/asset/jewelry-box-probably-from-the-worksh... (the golden rectangles are not golden rectangles, but the filigree therein looks similar to: https://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jan/... )
Jewelry boxes are a good target for incorporating vanity, or if religion is a better selling point, possibly try looking at Catholic tabernacles.
I feel the same about the idea of searching art for golden ratio as I do about searching iNaturalist for population curves of one particular shape. Aspect ratio is an extracted parameter. If your data set is large enough, you will hit 1.6 a few times, maybe enough to get a publication. If the audience is gullible, maybe they will buy the conclusion that golden ratio is important, but this is sleight of hand where *a lot* of other proportions have been ignored... Possibly even a worse bias than ballet, though, probably not.
If you want to get to the mathematical truth of what the golden ratio is, I would start with the character table of icosahedral symmetry, and then develop the real space matrix representation. After that, it is interesting to consider the generalization of Penrose's tiling to Danzer ABCK, see also:
https://demonstrations.wolfram.com/TransformationOfIcosahedralSolidsInZ15/
Then there is still the problem of "well it's not art". So what? Look what they did at Institute for Advanced study: https://www.ias.edu/idea-tags/concinnitas .
IAS is the house of the grand leaders and the trend setters, well in this case, they aren't setting the bar very high. When I made correlated figure 12 and Table IV for the "prelude" to my dissertation, at least I put some color into it! (There is also an Icosidodecahedron in there, V.G.1 page 28 & 29: https://github.com/bradklee/Dissertation/blob/master/Prelude/Prelude.pdf, see also: https://oeis.org/A318495)
--Brad
On Apr 26, 2020, at 11:34 AM, Henry Baker <hbaker1@pipeline.com> wrote: Yes, this has been done many, many times before...
participants (9)
-
Adam P. Goucher -
Brad Klee -
George Hart -
Henry Baker -
Hilarie Orman -
James Buddenhagen -
Kerry Mitchell -
Veit Elser -
Éric Angelini