Can Math Explain How Animals Get Their Patterns?
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- Опубліковано 3 січ 2025
- How Alan Turing's Reaction-Diffusion Model Simulates Patterns in Nature
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If you liked this video, we think you might also like this:
Reaction Diffusion Simulation (Gray-Scott model)
pmneila.github...
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Credits (and Twitter handles):
Script Writer: Rachel Becker (@RA_Becks)
Script Editor: Emily Elert (@eelert)
Video Illustrator: Ever Salazar (@eversalazar)
Video Director: Emily Elert (@eelert)
Video Narrator: Emily Elert (@eelert)
With Contributions From: Henry Reich, Alex Reich, Kate Yoshida, Omkar Bhagat, Peter Reich, David Goldenberg
Music by: Nathaniel Schroeder: / drschroeder
Also, special thanks to the following scientists:
Greg Barsh: Investigator, HudsonAlpha Institute for Biotechnology (goo.gl/RMD8o9)
Jeremy Green: Professor of developmental biology, King’s College London (goo.gl/Qcn8Ay)
Thomas Hiscock: Graduate student in systems biology, Harvard University (goo.gl/RbAWIy)
Shigeru Kondo: Professor, Osaka University (goo.gl/uQ2wYO)
James Sharpe: Coordinator of EMBL-CRG Systems Biology Unit and ICREA research professor (goo.gl/QCGul8)
Ian Stewart: Emeritus professor of mathematics, University of Warwick and author of The Mathematics of Life (goo.gl/rGR1R0)
Thomas Woolley: Postdoctoral scientist, St John's College Oxford (goo.gl/B4FZNn)
Image Credits:
Mouse palate images provided courtesy of Jeremy Green, King’s College London.
Digit patterns image provided courtesy of Luciano Marcon and Jelena Raspopovic.
Angelfish and zebrafish images provided courtesy of Shigeru Kondo.
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Here are some handy keywords to get your googling started:
Reaction-diffusion system: A hypothetical system in which multiple chemical substances diffuse through a defined space at different rates and react with one another, thereby generating a pattern.
Turing pattern: A periodic pattern that forms in a space where the initial distribution of ‘activator’ and ‘inhibitor’ is the same.
Morphogenesis: The processes during development that give rise to the form or shape of the organism or a structure
Alan Turing: Alan Turing was a British mathematician and the father of modern computer science. During World War II, he broke Germany’s Enigma code used to encrypt communications.
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References:
Economou, A. D., Ohazama, A., Porntaveetus, T., Sharpe, P. T., Kondo, S., Basson, M. A., … Green, J. B. A. (2012). Periodic stripe formation by a Turing-mechanism operating at growth zones in the mammalian palate. Nature Genetics, 44(3), 348-351. doi.org/10.1038...
Economou, A. D., & Green, J. B. (2014). Modelling from the experimental developmental biologists viewpoint. Seminars in Cell & Developmental Biology, 35, 58-65. doi:10.1016/j.semcdb.2014.07.006
Green, J. B., & Sharpe, J. (2015). Positional information and reaction-diffusion: Two big ideas in developmental biology combine.Development, 142(7), 1203-1211. doi:10.1242/dev.114991
Kimura, Y. T. (2016, May 24). The mathematics of patterns. Retrieved from www.theshapeofm...
Kimura, Y. T. (2014). The Mathematics of Patterns: The modeling and analysis of reaction-diffusion equations (Thesis, Princeton University). Http://www.pacm.prince....
Kondo, S., & Asai, R. (1995). A reaction-diffusion wave on the skin of the marine angelfish Pomacanthus. Nature, 376(6543), 765-768. doi:10.1038/376765a0
Kondo, S., & Miura, T. (2010). Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation. Science, 329(5999), 1616-1620. doi:10.1126/science.1179047
Marcon, L., & Sharpe, J. (2012). Turing patterns in development: What about the horse part? Current Opinion in Genetics & Development, 22(6), 578-584. doi:10.1016/j.gde.2012.11.013
Raspopovic, J., Marcon, L., Russo, L., & Sharpe, J. (2014). Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients. Science, 345(6196), 566-570. doi:10.1126/science.1252960
Stewart, I. (2012). The mathematics of life. Philadelphia, PA: Basic Books. (goo.gl/IOagrs)
Turing, A. M. (1952). The Chemical Basis of Morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 237(641), 37-72. Retrieved from www.dna.caltech...
If you want to play with some reaction diffusion models, try this interactive: pmneila.github.io/jsexp/grayscott/
Huh, this one doesn't seem to reach an equilibrium.
Feed rate: 0.03
Death rate: 0.06
That was fun, thank you :D
Isnt it a bit missleading to call him the inventor of computers?
... yet again.. inventor of software seems just as missleading xD
And meanwhile, both are right at some level.
da fuq is this :^)
Where can I get the code used for that ?
BitsAndBites
Maybe look at the math of the Gray-Scott model
"Sonic Hedgehog"
Scientific terms at their finest!
Hahah
shh bby is ok
Gotta go fast
Sanic
Read "Your Inner Fish" by Neil Shubin! It dives into how fish and humans are alike, and there's a lot about how Sonic hedgehog works in flies and humans.
It's short and I read it in Junior year, and it's great!
So wait, you're telling me that a scientist out there found a protein in mice embryo and decided to name it sonic the hedgehog? I'm not even mad that's amazing!
Actually it's called "Sonic hedgehog" Without the "The" in the middle :P
You should look at more protein names, specially from fruit fly. People from diverse backgrounds have done the research and made an eclectic mix of names.
Marwan Ahmed The gene was initially developed in fruit flies; it was named that because a certain mutated version caused the fly to develop spikes all over it, like a hedgehog.
Everyone: **looking at the comment**
Me: **looking at the current number of comments**
Fr
"..a protein called Sonic Hedgehog...."
The one & only protein I'll ever remember.
Mephistahpheles No reply’s until know
Why
;w;
@@vegancheese2999 his account is 5 yrs old, so, he probably doesn't use it anymore. Please explain the joke he made.
@@elianaa5286 That would make a lot of sense unlike the joke. I don’t know the context of the joke so it probably makes less sense to me.
TURING PATTERNS! I've written a paper on these before. They are unbelievably clever
The Enigma Machine wasn't what Turing invented, the Enigma Machine was the cipher machine used by the Nazis and it was invented by Arthur Schwernius in 1926. What Turing did was build a computational machine called Christopher to crack the Enigma machine, based on the Bombe machines created by Marian Rejewski a few years earlier.
Luke Koziol Yep. Poland had actually cracked the Enigma code before the war started, but right before the invasion the Nazis upgraded the machines from using three rotors to five, and since you need a Bombe for every rotor permutation, the Poles would have had to build fifty-four more, which they didn't have time to do.
I'm currently workong on a masters thesis on mathematical modelling, and your collection of sources is soo helpful!! Thank you so much.
0:28 DRAGONITE!! *everyone runs towards it*
same thought
Same thought.
fuck yeah
Still be awsome. Just really weak. Id say i had it but never show the cp if i could
I know right
12 seconds ago? but comments 5 minutes ago? TEACH ME
Maybe a YT glitch or maybe patrons get sneak peeks before videos go live ;D
Can confirm, I'm a patron :D
I smell a CONSPIRACY!!!!
time travel
Probably Patreon.
was that a dragonite?
dragonite with charizard wings
+Eka Ramdani true, they are really big for a dragonite
Scientist still doesn't know how the Dragonite are able to fly, much like the bumble bee.
+sevret313 Dragonite doesn't care what people think
+sevret313 we know how the bumblebee flies. Instead of just flapping its wings up and down, it uses circular motions with its wings.
Huh, so it's basically a PDE model. Wish they showed this in class instead of just heat and waves.
I know right? You'd think with all the applications of PDE's that something interesting can be taught from them in a college course.
Basically yeah but i found these (Turing Instabilities) harder than analysing the Helmholtz equation in a semi infinity domain (also pretty tough).
Tl;dr
Be careful what you wish for.
This reminds me of "The game of life" because that game creates patters as well if you bend the rules in the right way. It's not the board game but a mathematical game that has the environment effect everything around it. If you want to know more about it I know Numberphile has a video on it. It's a fun game to play and it has some interesting and fun outcomes of you bend the rules a little. There are also some apps that will simulate it for you. It's really cool!
A note about the Sonic Hedge Hog protein, it's actually involved with some serious and fatal diseases. You can imagine it's not super fun for a doctor to tell someone they're going to die because of a mutation in their Sonic Hedge Hog proteins. Fun Fact: it's inhibitor is called Robotnikin.
Interesting video, and interesting fusion of Dragonite and Spyro the Dragon. Both are great!
This is so cool! I had no idea that systems analysis had this particular application! Nature is awesome! :D
Regarding the fact that it seems to have mixed results, I'm reminded of Rational Choice modeling in economics: Perhaps these will allow us to model certain elements of reality without actually capturing the underlying mechanisms with 100% fidelity. Or, as I've heard some economists say: "Use your models but don't believe them."
Destroy the inhibitor and you get super minions
Destroy the inhibitor and you are able to warp to another star system.
good one
Teammates want kills
So that's why inhibitor sounds so familiar.
May i ask for the sauce from your pfp
2:42 Whoever named it that, thank you.
That is the solution to generating procedural textures I always wanted! Thank you !
The dragon at 0:27 has the color scheme of a Dragonite. That's incredible.
One biologist must have been quite the fan of the most famous blue hedgehog...
MinuteEarth at it's finest.
lol @ Sonic the Hedgehog! XD
Who the heck decided to name an INHIBITOR after him of all things?
ikr xD
Apparently, some doctors had embarassing situations when consulting patients with a gene mutation that coded for sonic hedgehog. In often a very serious situation, the doctor would have to tell them that they have a problem with their sonic hedgehog.
I think a lot more people would be interested in science if everything had more fun names like that.
Science would also cease to become science.
+smurfyday How?
Happy to see a CS legend on MinuteEarth
I finished reading the book you mentioned in the Audible ad a couple weeks back.
i like that you actually had stuff on turings blackborad that has beef wiped off before the video
And that, my friends, is why I'm on UA-cam ! Thanks for this sooo interresting video ! :D
turing has to be my favourite mathematician/scientist by now
Beautifully explained with necessary visuals
0:09 For a science channel that was awfully inaccurate. It would have been just as easy to say "a famous computer scientist" or even "a major pioneer of computer science".
Always a pleasure hearing Emily narrate a video.
Did you know that humans have these patterns as well, but we can't see them. There is a condition that exists that basically causes your body to be covered with so many freckles that it reveals said pattern. It's unique to each person too. Sometimes stripes, sometime splotches, and spots, or rings.
So my skin is a PREDITOR and my freckles and birthmarks are PREY
Predator*
no
And your hair is an Alien
Tf no lol. The predator-prey relationship was just used as a metaphor to describe the relationship between activators and inhibitors easier. Have no idea why you think your skin is a predator.
That Dragonite reference. I love this channel so much
Great video! I've never heard this about Alan Turing.
I don't know about anyone else, but that red/blue labyrinth patter absolutely destroyed my eyes. Great video though!
*pattern
+Anson Chan yes it did😣
You can edit comments by going to the three dots on the comment and select "edit"
+Omnilatent I'm on mobile.
Turing was a true genius! :)
what kind of calculus is that at 2:13? Looks likes derivatives but the symbol is different, can someone explain pls?
Multivariable calculus, calculus on functions with more than one variable.
Yeah, they're called partial derivatives (cause you only derive with respect to one from multiple variables).
Could this also apply to things like your fingerprint pattern?
That was exceptionally interesting.
Thanks for the great video!
The reaction diffusion simulation in the description is pretty cool, check it out guys :D a feed rate of 0.031 and a death rate of 0.064 gives an effect kind of like mitosis, which generates evenly spaced dots that self-replicate :D
"alan turning, the guy who invented computers"
how anxious were you, reading that simplified-for-time narration and knowing it'd immediately get pounced upon by anyone wanting to look smart in the comments section?
If you want to see a different way of forming patterns (through selective cell division) check out this simulator I made: bl.ocks.org/MattWoelk/5687467
Follow the "Pattern Formation" instructions to make it work. (refresh to start a new one)
The most beautiful idea I have heard.
In 0:39 or 0:36 the dragon look like dragonite from pokemon
I love how you hide Pokemon's in every videos.😁
The cheater got its spots by copying the tiger's homework but changing it a bit.
These kind of models (Activator-Inhibitor) can be applied also to plenty of other fields/applications
Hello MinuteEarth, could you tell me the author(s) of 2:39-2:55 section. For science puproses. Thank You.
0:27
*charizard and dragonite fuzion!*
Ian Stewart gave a great lecture on this at a Discworld Convention.
what are these formulas called? I want to try to model them in JavaScript but I want to see if it's been done before
They are reaction diffusion models. They have been done. Actually, check the video description for a nice simulation (the third link)
look up p5.js reaction diffusion on youtube, the guy shows how to implement them
If there were activators and inhibitors responsible for animals' patterns there should be some mutations appearing occasionally. Causing the two agents to distribute slightly differently. So there would be very rare striped giraffes and spotted tigers and so on.
0:19 sooooo simple
Minute Physics:
Teaches The Unthinkable
Also Minute Physics:
Shows An Old Cow From Alan Turing's Time To Now Still Alive
(Defying Life Expectancy O-O)
3:12
*hypothesis, not theory
close enough, now that Game Theory has ruined this term...
No you're completely wrong.. It was a good attempt at looking smart but no. It is a theory... Try researching, or just simply Google the definition before trying to look smart😂
Except the standard meaning of the word "theory" differs from the scientific one (we are roughly 90+% sure that this is how it works, but since everything is disprovable, we can't call it anything more than a theory). In this case, the word "hypothesis" (someone thinks this is how it works, but we are not convinced) is a better term.
+Bots Magots holy irony.
***** ha ha yup you got me.... No, Theory was used correctly in this video, none of you can argue against me and Toomas Tennisberg I somewhat agree with you, except for "since everything is disprovable" That is incorrect, evolution isn't technically "100% proven" but that doesn't mean everything is disprovable and it doesn't mean that evolution is a hypothesis,
To summarize this comment: Theory was used correctly in this video :)
Wouldn't that be a hypothesis, not a theory?
As this is biology, a science, I think the word "hypothesis" should've used.
No, theory is correct. In science a theory is used to describe how a system in nature works or came about. It combines observations, facts and laws. A hypothesis is used to test the strength of a theory.
Shh, "theory" sounds more cool.
No, because the theory is backed by evidence. A hypothesis has little to no evidence to support, because it is basically just an educated guess.
SomethingIronic A hypothesis is one idea. A theory is a collection of hypotheses.
The guy who invented computers stole Levi's hair
0:11 Alan Turing did not invent computers, he made advancements in programming algorithms. Credit should go to Ada Lovelace & Charles Babbage.
you should make a simulation of this where you get to play around with the activator in ihibitor to create different patterns
This is what I live for, I love knowledge.
0:26 I think MinuteEarth just gained some new respect.
Also in some species, like cats for example, X-inactivation aka Lyonization (a natural phenomenon that happens in all female mammals) is responsible for these color patterns in females. Most of the time it's random.
Dragonite 2: 1:26
Didn't know Turing had developed this theory. Nice
Clearly, the cheetah got its stripes by demonstrating modern behaviour throughout its many years of military service.
that dragonite though
Some sea snail shells resembles cellular automaton with simple rules like Conus textile.
That's amazing, Thanks for the information!
I like how the animals look all peeved in the thumbnail for some reason
how would this work with a leopard's spots? (they have groups of spots not random spots like a cheetah)
Incredible idea. Maybe this theory could explain the pattern of male pattern baldness?
very good analogy
Any more information about why the inhibitor's range expands faster, I understand the fox analogy but why is this so in chemical morphogenesis. Thank you.
Thank you ! A wonderful video !!
For some reason at 0:12 i thought the binary going through the machine said something so i put it through a binary decoder and got
*Ô*
𝘛𝘣𝘩 𝘪 𝘥𝘪𝘥𝘯𝘵 𝘬𝘯𝘰𝘸 𝘸𝘩𝘢𝘵 𝘪 𝘦𝘹𝘱𝘦𝘤𝘵𝘦𝘥 𝘣𝘶𝘵 𝘩𝘦𝘺
Love the video, just one thing: Math cannot 'explain', math cannot 'do' anything - it's a language that an intelligent life, as yourself, can proficiently use to explain something, as you did. It doesn't "describe what we see in the real world", it offers a model for what we see. We should not confuse the tool (the mathematical language and methods) with what it may enable a computing agent to do, like the mathematician forwarding a model, algorithm for calculation of pattern, etc.
The difference is very important in case you don't want to commit to a platonistic view of mathematics. I mean the view that math describes some sort of abstract eternal reality, call it Plato's Museum of Abstract Forms, right next to the Archive of Moral Codes in Heaven.
Oh, and a hurray(!) for Turing being so freaking smart.
But I still wonder,the Cheetah has stripes and spots,so does this mean that there are different spots where there can be more blue circles and red triangles in the body of the Cheetah?
theoroetical animal of choice: pokemon
**pokemon later at **1:19** earns a new spot**
pokemon creators: NOOO WUT ARE U DOING TO OUR POKEMON
theoroetical yes
I didn't understood the comparison of the inhibitor and activator with the foxes and bunnies, can somebody explain it to me? Does the inhibitor feed on the activator or something like that?
I just think that different types of colours and patterns help the animals in camouflage either to catch prey or hide from hunters
I heard that giraffe's spots (or between them) were aligned with blood vessels.
Neat stuff - learned something new today.
this video broke my brain. thanks
That BUT at 2:09 was strangely cuter
awesome video as usual! has anyone told you, that your voice remind them of Barbra Dunkelman from roosterteeth
This is also the theory of our human fingerprint ridge patterns
This is so interesting!
Not really accurate to say that Alan Turing invented computers, more that he created some of the math necessary for the modern ideas of computation, but sure. Boole, Babbage, Lovelace, and Zuse did work before hand. Konrad Zuse's Z3 was the first actually built Turing Complete computer, even before the idea of Turing Completeness existed (although Babbage's Analytic Engine would have worked, had it been built). Alan Turing did fantastic work, but don't credit him for something that he didn't do.
I know your being sponsored but you should listen to the horses of oak valley ranch by Jane smiley, it’s so good if you like horses and stuff a lil back in the day, me and my mom love it!
@MinuteEarth at 3:12 you say observations inspired a theory. Please say hypothesis instead of theory because theory in science means something that is proven. This was apparently not proven yet. So it's a hypothesis.
Math can explain everything but we may not have enough data for the formulas. Any determinist will tell you that or something like that.
Could the "clumping" cause fingerprints?
Sonic: shhhhhhhh!
At 1:26 that is a dragonite
Dragonite and Charizard doing a Potara fusion
That clicking sound really bothered me, But the video was GREAT!
Pretty interesting video, thanks! :)
Well I found the right SPOT to learn
was that a dragonite? 0:25
Just like animals and fish,can we find patterns or spots on dinosaur skins by using same method 🤔
morphogenesis is fascinating