Butterflies and Gyroids - Numberphile
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- Опубликовано: 8 сен 2024
- Dr Sabetta Matsumoto discusses some of the mathematics of colour in nature, including butterfly wings and soap films.
More links & stuff in full description below ↓↓↓
Dr Matsumoto's group at Georgia Tech: matsumoto.gatec...
And her Twitter: / sabetta_
Previous video with Sabetta on Numberphile: • The Girl with the Hype...
Brady looks at butterflies on Objectivity: • The Butterfly Collecto...
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Sabetta looks calm and anxious at the same time in the thumbnails.
Comfortable sounding nervous.
This is Bragg's Law, in geology we use it in X-ray diffraction to analyse crystal structure.
I just remember it from optics as "the one where theta's in the wrong place" ;)
@@alynames7171 Same lol
I'm a materials science student and we just had a lecture about structural colors! Fascinating!:)
same here man felt so ready for would be
I just saw a interesting paper about giroids.
??
@@Triantalex sorry?
This video is the perfect integration of math, physics and chemistry
AND biology!
AND nail art!
♥️
and science
And 3d printing
This was my response when my date said, "What a pretty butterfly." I didn't get a second date.
Then they didn't deserve you ;)
Still, worth it.
I have done this on a date before (to the museum, and at an insectarium). If people can't at least appreciate your excitement when you're talking about your interests, then they weren't the right person.
@Nobody Knows More About Losing Than Donald Trump No way dude. I always derive on the first date.
@@bsharpmajorscale Drink and derive! YOLO
The derivation wasn't complete. You have to take the phase shift of pi into consideration that happens at the optically denser medium.
In case of soap there will also be a change in angle of the light rays caused by different density between air and water/soap
Naughty mathematicians completely ignoring the refractive indices of the medium.
That's a trivial detail for the basic thing happening here. It changes exactly how far apart the reflectors need to be, but the diagram shows the important part.
@@jursamaj I see what you did there ;-)
Exactly what i was thinking, but yeah, it is trivial
Understood like 5 words
Right, but that is unchanging so it works as it works.
I've been fascinated with gyroids for years, they're an absolutely fascinating triply periodic minimal surface! I'm so glad to see this pop up over and over
This is rally interesting. I hope Dr. Matsumoto comes back.
Gyroid infill is my new favorite 3d print infill.
That came out of the blue.
@@harriehausenman8623 terrible, 10/10
"What this butterfly, my nail polish, and soap bubbles have in common"
They all taste delicious
Wtf
@@reedplaysgames he's right though
Periodic videos should do a crossover and talk about how this is related to highly conjugated molecules. I dont know how they are related, but it stands to reason that they are. I learned from a chemical perspective that color comes from conjugated molecules. Does color come from how those molecules stack like the video suggests? That is the question.
(pi-)Conjugated molecules (organic dyes) get their colors/fluorescence due to electronic effects, related to things such as excited states and (molecular) orbital coupling. This is fundamentally different from the structural color effects explained in this video.
Amazing explanation! Really made diffraction accessible to a broad audience
One small note: chitin is not a protein :) 9:24
Just FYI, chitin is a polysaccharide not a protein.
...ok?
Why did they give it a proteiny name?
@@Gmackematix It was forming things that act like a coat or a tunic and the people getting to decide on the name were French.
At least that's my best guess.
@@jounik Oh yes, 'chitine' a French word from the Latinised Greek word for a coat. I suppose the fact that it is functionally similar to keratin and that its structure wasn't really discovered until the 1920s also helped.
So cool. Animations make everything more understandable but that camera view angles...
yeah that looks so much forced and less creative
11:01 has some serious Uncut Gems energy. At least it was just a fingernail we were zooming into.
Reflections invert the wave, effectively pushing it along by half a wavelength.
But I guess if all the rays you're looking at are reflective it doesn't matter.
"Cell membranes are just fancy soap films."
~Numberphile 2020
Not funny
I mean, they basically are though.
The name "Gyroid" reminds me to a special decoration-object in the "Animal Crossing" Nintendo-game series.
In there it is a set of dancing, noise-making sculptures with a cylindric body and angeled arms (some of them remind me to tiki-mask-poles).
They can be dug out of the ground like the also existing fossils in the player´s environment.
As usual, one like button is simply not enough to express how engaging and fascinating Brady's videos are. Thanks and cheers, mate!
Lexus used Structural Colour in their Structural Blue paint. The video about that is also super fascinating
Do you know if Lexus did that paint before or after BASF created Mystic (a structural color paint) for the 1996 Ford Mustang SVT?
@@jpe1 after. It was made for the 2018 Lexus LC
I love Gyroids in Animal Crossing
Blathers: *sees an emperor butterfly* Eek!
*Blathers left the chat*
*Gyroids entered the chat*
Came to this video to get away from studying for my physics final.... there is no escape!! lol
i came to this video too
Once I saw a car with changing colors like that and for a moment I thought I drank from the wrong cup of tea.
We had an airplane painted with some special paint at the factory once. Golden from one side, shiny pink from another.
If the car was a 1996 Ford SVT Mustang, and the paint was from the factory, it was a color called “mystic” and the iridescent color was indeed structural color like a soap bubble, but specifically the paint color comes from microscopic ultra-thin layers of interference film developed by BASF, called ChromaFlair (the trademark for which is held by Flex Products). By adjusting the composition and thickness of the flakes the color of the resulting paint can be adjusted.
Lovely video! Great to see how you can combine biology, physics, math, chemistry all in one go!
This is amazing stuff.
I know it may be more difficult than some of your other videos, but it's awesome to see wave forms getting some attention, and it's all wrapped up in how it works in the real world.
I'm also led to understand that nature doesn't create blue pigment, and seeing how it's done (in this case) is really cool.
I never understood the difference between pigment vs. structural. Isn't pigment structural as well if you zoom in far enough?
One is because of the affect the structure has on the incoming light and the other is because of the structure of the molecular orbitals allowing certain absorption spectra. But yes effectively they are both 'structural', just at different scales and by different physical processes.
With a pigment, it's more the difference in energy levels between states of some of the electrons in the molecule. So the "structural" effect there has to do with the configuration of the electron's waves, instead of the photon's waves. Structural color will do what it does even if there is no particular resonance in the molecules.
How can you talk about this without mentioning the name William Lawrence Bragg even once? You even mentioned crystal lattices, but no mention of Bragg and his work regarding crystal analysis with x-rays.
Loving this channel. 🤗🤗🤗
My background is in Physics, though I work in Meteorology now - but my dissertation was all about DBRs and structural colouration. I think I'll just refer people to this video now so they don't have to listen to me talk about it :')
I could see a time, where you could resin 3d print colour with a high enough printing resolution.
SimplyNailogical should see this 😊
After refraction it wouldn't be angle theta as light is travelling from two different medium. So it bends inwards
I hope you don't have accreditations.
Both theta's turn into new angles after considering this. So we call those new angles theta, and this whole thing works exactly as-is
This is as if maths, biology, physics and chemistry had a baby.
Nature doesn’t divide itself into compartments, after all. The compartments exist only inside our heads.
Only if Biology decided to ignore itself and allowed 4 different parents to contribute to 1 child....
Physics and Chemistry are just offshoots of Mathematics(they rely heavily, very very heavily, on Math) Sooo.. Why not just say Math/s and Biology?..
Oh nvm I get it.. I see the comment from 5 hours before yours talking about the perfect integration of math, physics, and chemistry. With a reply stating to include biology too..
So yeah... I see what you're doin..
shrek is a liar! If he actually had layers, he would be glistening all the time
He glistens at radio frequencies
@@MushookieMan nice save xD
But honesty don't we all??
translucent layers tho?
Thanks ! Happy new year !
Is there no refraction when light passes through the layers? Changing the angle?
There is but its all the same material so it doesnt change the math. It all cancels out
Numberphile has currently 3.56 million subs, while 3Blue1Brown has 3.35 million. Numberphile only has ~ 200 thousand more subscribers than 3Blue1Brown. I expect that 3Blue1Brown will have more subscribers than Numberphile by June 2021.
@Calum Tatum and numberphile will be surpassed by 3blue1brown by mid February if the latter is run by Mr. Beast.
Seems a big jump at 7:00 in the algebra. I worked it out in my head and you have you remember that AB and BC are equal so:
2AB = nλ + AD
2AB = nλ + 2ABcos^2(θ)
2AB(1 - cos^2(θ)) = nλ
2AB(sin^2(θ)) = nλ (by pythagoras)
2dsin^2(θ)/sin(θ) = nλ
2dsin(θ) = nλ
I think I understand the intuition behind these structural colours. But every time I see a video on the topic, I'm left with the question "what does a pigment do??". What does it mean to say a pigment absorbs some wave lengths and reflects the rest? What is the physics of it? Anyone got a pointer?
Getting the right colour is based on itd pigment. Thanks
Excellent video. This is fascinating stuff!
can you too see the eyes forming in the butterfly wings when they aren't completely blue?? like in 9:41 and at the very beginning of the video, at 0:32 you can see it very clearly
The Smarter Every Day channel took a closer look into the butterfly wings. It is a fascinating concept.
Dragonflies don't use structural colour so they fade away to boring browns after death, you can't preserve the colours as with butterfly wings... (I bet there are some exceptions, nature is too inventive :)
Yay, Bragg reflection!
would the wave not refract after hitting the first layer boundary in the soap bubble? I would have thought the second two angles would be different to the first two you labelled theta?
So could you 3D print a gyroid that has structural color? Would it need to be made of special materials or if you printed a billion of them super tiny would it have a color?
To everyone complaining about refractive indexes and the like, one must remember this is the land of perfectly homogeneous spherical cows.
Why this video not stuck at 301 views????
This takes me back to my phyics classes in school but without the butterflies, instead we had Newton's Rings which work in a similar way
So interesting. Thanks for another great video.
I love this
Remembering my 2nd year of honors, optics was fun.
First the Daleks, then the Cybermen, now the Gyroids. Will the Doctor never be able to relax for even a moment?
Lexus managed to make a structural blue automotive paint and uses it on limited editions of their higher end models
It was a limited edition because they ran out of nail polish
Top notch Numberphile video. Very, very well done!
The physical explanation is not quite correct(It ignores how the light path changes as it is moving through the different layers. Also, the generally accepted explanation of rainbow-like colors seen in soap bubbles is that the thickness of the soap layer is changing, not that the angle of incidence is changing. The actual model of a soap bubble really should include a single layer of soap surrounded by two layers of air. One can use such a model to describe everything that is happening.
Are there structures that produce other colors besides the morpho blue?
If you change the size of the gyroid's repeating shape, you'll get different wavelengths.
Is that diagram simplified? Water has a higher index of refraction than air, so the slopes of AB and BC should be steeper than the slope of AD. (Aside from using different values for ɸ, the algorithm should be the same, though.)
Exactly
A number a day keeps the depression away
The titles of these videos hook me so badly
Is this a case of single photons interfering with themselves? Intuitively it seems like if structural coloration was the result of different photons interfering with each other, the light source would have coherence? Thanks for any replies.
It's always a photon intefering with itself, one by one.
@@Milan_Openfeint Thanks for the response!
super fascinating! colors are great
Wow, who knew? I sure didn't. This was a very surprising twist on something I thought I understood before, the twist happening when Dr. Matsumoto explains that the crystal structure is roughly 1000x more fine than the structure employed by the butterfly, and then..... I love your videos and your guests who challenge my mind and teach me something new each time!! Bravo!
One of my FAVE topics! 👏🏼🌟❤️
Blue Morpho, we meet again..
Go Team Venture!
awesome 3d printing!
This pattern can also be used in 3D printing slicer software as the infill for your 3D models where it can help increase the strength of parts while still printing relatively quickly.
If you'd like to know more, check out the infill strength test and comparisons by CNC Kitchen.
I searched for Animal Crossing gyroids…
HI!
excellent content
Binky Barnes would be shedding a tear for that butterfly.
👍
9:19 does this butterfly have color of the dress?
I didn't see a blue butterfly, I saw a gold moth
I had to watch this muted with subtitles because that voice is just excruciating.
Love the music
Elisabetta's cadence reminds of Reviewbrah.
Interesting observation.
I thought this was about nail art 💅and ended up scratching my head trying to understand 😂
It is about nail art!
"ended up scratching my head trying to understand" - that's another type of nail art.
@@dlevi67 More of a performance art though. :)
Very interesting!
The first "soap" example is exactly the same thing geometrically as the Ted-Ed video on opals, right?
I bet Alan had been in the core in Astroneer when he made the music for this episode
I'm wondering if these mathematics are applied to raytracing in videogames?
Gyroid infill is best infill
But what's color of the original material with which the wing is made?
Some day those pictures and awards will go from the floor to the wall. But today is not that day. :P
This is fascinating!!!
I'm glad I'm this early
hi fellow GD player
😮
@@lumi2030 add me : ItzFrenz
@@frenzvalios ok!
That escalated fast
Bragg's law
He’s the only physics Nobel laureate we had at my uni. Stg I heard his name every fifteen minutes haha
It's always nice to see, but I found that this derivation of Bragg's law was slightly over complicated compared to other ways I've seen it derived. Still cool, nevertheless, but what do you think?
I clicked on this thinking it was an Animal Crossing video. Still interesting.
could you talk about the mathematic relationship between Butterfly's and Hurricanes?
Hello everyone! Can you recommend books that go into depth and width about trigonometry?
Hey the 8 years old video is stll at 301 views
Why is the video at an angle. Very distracting.
Maybe you have tilted chair
@@DANBOOO 0:55
bluejay feathers next?
I'm missing some sort of mathematical definition of the gyroid surface. Well, I guess I have the Internet at my fingertips...
This one was a nice break from counting
Amazing ❤️
Soap is an FFT analyzer of light :P
Seems like a lesson of Ray optics
Bragg's law of diffraction in miner details.
Dang, them butterflies be SMART.