Wow! First Ever Fractal Molecule Discovered Inside Bacteria...And It Works!
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- Опубликовано: 8 май 2024
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Hello and welcome! My name is Anton and in this video, we will talk about a discovery of the molecular fractal that's kind of mind blowing
Links:
www.nature.com/articles/s4158...
www.mpg.de/21811459/0410-terr...
Cosmic web: • First Direct Evidence ...
• Incredible First Image...
#fractal #biology #bacteria
0:00 Fractals in nature
2:05 Smallest fractal ever found
2:38 Bacteria where it was found
3:30 What fractal this is
4:30 What and why is this?
5:20 Problem with predicting proteins
6:20 How is this forming though?
7:35 What does it do inside the cell?
9:00 Conclusions
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Credit:
Simpsons contributor en.wikipedia.org/wiki/Fractal...
Ivar Leidus CC BY-SA 4.0 en.wikipedia.org/wiki/Fractal...
Bert Hickman - www.capturedlightning.com en.wikipedia.org/wiki/Fractal...
NASA www.flickr.com/photos/nasa2ex...
Rafael Ruggiero CC BY-SA 4.0 en.wikipedia.org/wiki/Fractal...
Akarpe CC BY-SA 3.0 en.wikipedia.org/wiki/Sierpiń...
Anthony Majanlahti - www.flickr.com/photos/antmoos... CC BY 2.0
Raul Gonzalez and Cheryl Kerfeld - www.kerfeldlab.org/images.html CC BY-SA 3.0 en.wikipedia.org/wiki/Synecho...
Depauwdrew777 en.wikipedia.org/wiki/Citrate...
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Наука
Uh oh. That Bacteria is about to get a cease and desist letter from Nintendo's legal team for copyright infringement. Lmao.
was about to say something about this, but ill upvote instead =p
🏆
if anything this means we can use the shit out of it because it is a naturally forming pattern
😂
I think those wonderful people who publish the papers with that nomaclature will get legal letters first
the fact that bacteria can triforce is WILD
▲
▲ ▲
Bacteria holding the molecule above it self :
"You obtain the fractal molecule, you can now fractalize"
Holy shit this brought me back wtffffff 😂😂😂
The legend of Synechococcus Elongatus
▲
▲ ▲
Oh no i messed it up...i guess im a newf......i will stop before people get mad.
I watch your channel regularly. Not in my wildest dreams would I have imagined that you would ever cover one of my papers. Love your work!
This is your study? What will be done after this discovery?
It's like the realization from musicians that Weird Al covered their song. That's how you know you've truly made it.
Cool discovery!🎉
@@illegal_space_alien 🤓 actually.... weird Al always asks for permissions before doing a parody xx
@@smellystinker4837 Then its like the realization from musicians that when Wierd Al asks permission to cover their song, thats how you know you've truly made it.
I’m a geologist and fractals are dominant in many geologic features. That’s why geologist’s photos always have something like a pen, notebook, person or car, etc., in them for scale, a little tiny fault can otherwise look the same as one 500 feet tall, for example.
Where is Link when we need him
Last I heard he was hosting a boxercise event called Hiyah Hyrule
It's a secret to everybody
It IS the Link
Hes ... uh... gone sorry
Apparently the Princess got kidnapped by Ganon....again. And this is just rumor but some chambermaids say she and 'Dorfie' text alot.
Mandelbrot would have lost his mind 😂😂😂 "I told ya ! I Told ya !!!"
❤
James Gleick too!
Maybe he's seen romanescu broccoli
That bacteria be living in the 2.5 dimension no cap
Check out the z axis of the Mandelbrot Set...and get your minds blown.
This is important as we are very close to using biology to build geometric structures at a molecular level, meaning we could grow filters, transistors and molecular scaffolds for stem cells.
Imagine your computer catching a virus
I think there’s already a PC build that uses mycelium and fungi colonies as parts on the cob for it... video up here on yt somewheres
Surveillance devices that report your real time sensory output to the authorities, immortality for rich people only, paper thin armor that can be applied to anything and makes everything so terrorism proof the current political hierarchy will potentially reign forever, right up until someone invents a munition with indestructible penetrators so small and so powerful they penetrate this armor and turn the human being beneath into a cloud of dust and juices that both intermixes and boils such that it turns into a substance the boys in R&D have been calling "slurm".
@@Distress.Yeah. Imagine that.
How crazy.
The Legend of Bacteria: Fractal of the Wild is a classic. Love that one.
If Saturn can have a hexagon, fractals in bacteria ought to be a cinch.
Hexagons are the bestagons! Saturn had taste.
@JamesDavy2009 😋😋😋
If you are talking about the weird storm on the saturn pole you are wrong... It have not a perfect hexagonal form and it have a perfectly reasonably explanation...
@@adriangogioiu2611I don’t think you have the brain capacity to understand the comment! 😮
What is the reason?@@adriangogioiu2611
Sierpinski is also a shape used for cell phone antennas. Maybe the bacteria use these as teenie weenie communication devices.
Whoa whoa, you can't just say things like that, or biologists might start falling off of their chairs.
interesting point! reinforces the imagined line between pathology and ‘daemonic’ interference. if bacteria etc in some sense have hive-like properties or propagate information in the ether as if a super organism. fascinating.
Is this the dreaded 5G infections they're talking about?
@@hm09235nd complex life did evolve as mobile chassis for bacteria to get around
Interesting
Thanks! Long overdue. Beautiful pics tonight and great narration
Anton should be at 1.8 billion subs. Such an undiscovered gem.
Billions must learn
This video made my day. Currently I'm writing my thesis on modeling cities with fractals and I noticed that they appear in multiple and unexpected places. Whether they can serve biological functions or not, they are beautiful and I'm glad that the scientific community continues to study them. Wonderful shapes for wonderful intelligences in a wonderful world.
Thats really interesting! I want an entire city made of fractals! But maybe that already exists🤔 what do you think?
oh thats interesting! i have been explaining reaction diffusion and turing patterns by looking at european city growth..do you think these perspectives have synergies?
I think for space and cost it would theoretically maximize efficiency but in actual practice, I think it would be a nightmare. It’s would be like going to HOA housing block where all the houses are the same and you can’t even remember which house is your own from a glance. I think it would make your grubhub order about 10x longer lol
What/where are these multiple and unexpected places?
Yes, please explain more!
The comments section on this video includes:
60% Zelda references
35% New Agers talking woo
5% Other comments
Everyone loves fractals!
Ah yes, the obligatory reference to 'woo' when anything crops up that suggests a possible contradiction of the culturally pre-determined dogmatism of the philosophical physicalism of scientism (as distinct from genuine science). But real science is more open-minded and open-ended, with no need to adopt defensive postures.
@richardoldfield6714 No that's incorrect. Science is not an open minded process, science is the process of taking a definitive fact and using observation for understanding. Throwing theories at the window isn't science. Science is the not the process of just imagining ideas, it's the process of study and examination.
Something like MOND or string theory is science purely because each explain things were currently don't understand, even if both are likely wrong. Your explanation has to at least be logical on the surface.
@@Skylancer727Incorrect. Science *is* an open-minded process. It does not rule out things without strong evidence to do so ... and even then is open to the possibility of new, contrary evidence emerging later. What genuine science does *not* do is describe as 'woo' anything which conflicts with philosophical physicalism, even if that that philosophy is mainstream within science currently.
You act like no aspect of the perennial wisdom has penetrated the sanctum of your cranium. Nearly all discovery is rediscovery. How much of today is like previous days, and how much should you unlearn to be as smart as your ancestors?
And 81 years ago, today, the 19th of April, Alexander Hoffman took LSD for the first time in history shortly after discovering and synthesizing it.
Power, Wisdom, Courage
Life is fractal
Time is fractal
Universe is fractal .
phrases that arent true often end in the word... fractal
You're fractal.
@@theendoftheline stop living in the dark age . Time is not linear past present futur
Universe look like a brain
Trees ,blood vessels are clearly fractal
@@sabinrawr yes look my blood vessels and nerve system. Fractal
Spirit finds a way - science is only but a tiny whisp of Spirit
Triforce fractal... Wow
Yer interesting idea, Tri force fractal. It had me thinking about the inner triangle and the helix and the symbol of the Absolute found in the Enneagram model representative of the synergetic properties of The Nine Energies.
It's way more reasonable to assume that this is just for slightly more efficient packing and unpacking of surplus enzymes for better control over metabolism.
It's an extremely durable structure with nearly maximal surface area; with fewer internal cavities, it would probably miss out on significant RF \ particulate interaction...
Because fractals and the golden ratio are the building blocks of the universe
It would be a hexagon or a circle for efficiency, not a triangle.
@@festerbutthexagons are composed of triangles I hope you realize that
So cool seeing your panoramic scanning abilities in action. From the macro to the micro, the reason why I donate to your site. Always a refreshing wake up call is one manner of expressing it. Thank
That feel when bacteria can triforce and I can't...
😂came here to say this
Yet...
That bacteria's adn is older and more ancient than yours. Did you get that? .YES .NO
@@DioDCynicUm, you mean DNA? Did I miss a joke?
On Windows Alt+30 is the triangle, that's the easy part. Don't use the space key to space out the upper triangle, a lot of websites will delete erroneous spaces at the beginnings of posts, use Alt+255, it produces a space that won't get cut out.
It definitely feels significant because of how it is perfect.
Every Time I Watch One of Antwon’s Wonderful Videos I Always Think is There Anything That He Has Not Studied About or Been in constant Awe of ? I think he is a Truly Gifted young man and Has a Never-ending Thirst of Learning !!!! We are Lucky to have him !!!
this comment could be an isekai anime title
@@RaynMaoAnton is one isekai MC with OP teaching research and informing powers, it's over 9000!!!
3:35 you can see it only links first-order Sierpinski triangles (triforces) together which aren't really fractals as they don't recur within themselves.
Bacteria wouldn't speak about the molecule. So we had to triforce.
Looks like the
ANDROMEDA STRAIN
Great book
@@kingdot2616 Indeed
My first thought as well.
Ya, this is really creepy! I watched the original movie many years ago and as a Biologist it gave me nightmares. It still does to this day. It was an incredibly accurate representation of how we do our work (minus the overkill on the sanitization of the human body).
@@allankolenovsky7028 Have you seen the movie "Warning Sign" from 1984? The lab accident at the beginning is a hoot
Once again, another great vid. Got to share this with my mate, it's right up his street. Congrats on the nearly 1.3 million subscribers. Keep it up you legend. Cheers Anton..
It's up his street? Your mate lives inside a cyanobacteria?
Fractals are common in crystalline structures. If you consider salts or sugars, fractals wouldn't be surprising.
Right, and with how quickly bacteria evolve I'm not surprised we're first seeing fractalling in them
Humans use that structure to build mobile phone antennas... Maybe bacterias have been doing the same for millenia XD
Beware the bacteria revolution. They've been monitoring our radio transmissions!
/s
It's the same shape as a micro receiver chip!!! Look up the video DNA is a fractal antenna 📡
I CAN FEEL THE 5G IN MY TUBERCULOSIS RIDDLED LUNGS AUUUUUGGGGHHHHHHHH
Something something, "phone home", something something.
Cashing in on that free 5G energy!
Just because other shapes do work does not mean that there is no reason for it. We just have not found the reason yet.
Yea its insane to think there is no reason for it. Nature doesn't waste a lot of effort, especially on something so complex. . .for NO reason. Its silly.
The reason is
_It's friggin' RAD_
the bottom line reason is 1.618 aka the divine ratio
Agreed! Not knowing the reason does not necessarily mean there isn't a good reason. Just in case anyone missed it/cares: Anton also said that a couple times, one of em is at 8:50 😊 🫶
??? Why would you talk about other BORING shapes at a time like this. Fun at parties you
Awesome post. I love your channel. Keep up the great work!
I remember the first time I watched a documentary on the Mandelbrot Set and for weeks afterward everywhere and everything I saw in nature was just fractals and it really freaked me out. It was like i could see the matrix... I was just looking at trees and seeing a formula and it freaked me out.
are you sure it wasn't LSD 😂
yeh when i was learning vectors it was the same
Yeah they're really everywhere.
Grow weed for a while, and you'll see many plants and trees start resembling buds.
Their shapes, I mean.
Not kidding, but that shit is funny cause it's such a stoner thing.
Huh, now I'm wondering if that's fractals lol.
Hope you returned to reality a bit 😂
I drained the toilet water in my trailer and the gas made me hallucinate these fractals. Warning: don’t drain raw sewage without a proper assmask .
Assmask?
That last sentence quoted out of context may be the greatest typo in human history.
What the hell...
Jenkem
Don't freebase fumes, especially not through your ass 💀
I have discovered that these tiny little fractals make me happy
Looking or gazing upon the art self assembly of Fractals seems magical and peaceful.
Love love love your videos Anton, keep it up!
The fractals brought on by DMT are amazing
That guy from Gem & Jam of All Gas no Breaks, the one that smoked G funk with the homeless down the bridge be loosing his damn mind when he sees this
Thank you, Anton, for providing us with some positive news in our lives. Sure is neat times we live in.
Bravo, Anton. This is astounding and really interesting! Thank you
Hey Anton! First of all, thank you for your content! It is very interresting and educational (gonna show my kids in future to learn english and science studies!). I've recently seen video of russian blogger about "left and right" scientific nature. It came out that it is a lot of science in nature of left and right. This could be very interresting topic, expecially regarded to fractals nature!
Wish you all the best! Thanks again for your content!
There is no coincidence. We just haven't figured out what it means yet. Fractals are so cool!
I can tell how the ancients knew... magic mushrooms. Seeing fractals in one of the biggest common phenomena when consuming psychedelics. There is definitley a deeper meaning to it.
Yeah fractalization of everything you look at is so much fun.
Not a bad point, I wasn’t thinking of it like that but I agree
I've seen fractals as eyelid movies during a gong bath / sound healing. No drugs required. I also astral travelled on a meditation retreat so I'm probably atypical.
@@richardhall5489 do you want to buy a bridge?
@@Splozy
🤔
Once as a teenager I had an experience where I could see that the universe was largely built in the form of constantly changing fractals. Could see the patterns of the grass, the clouds, even the structure of the language from our brains into the air.
🍄🍄🍄
That's called LSD buddy, it's not good for you. 😂
DMT is very interesting.
@@kalebwhite3210oit’s not for everyone but it’s amazing
I've had similar experiences with psilocybin. It's wonderfully humbling to be reminded from time to time just how interconnected all things really are.
Will be looking forward to more news on the fractal enzyme. That design is beautiful!
Think of QR codes....so a Fractal is a 2.01-2.99 dimension of a long enzyme to be folded to occupy less 3d space ...fractal folding helps a lot since its like origami paper folding from Japan
fractals contain the whole within the part, a non linear function, like a hologram
I love this channel. Keeping us up to date on all new science in digestible bites.
I've been saying this for decades: Fractals are truth; Fractals are life.
The Mandelbrot set is OP.
Remarkable! And this fractal is not going unnoticed! Thank you wonderful person!
Fractals can perform information compression, so perhaps that's why they arise. I'd like to know if there's any evidence for gravitational or temporal fractals.
I've got a buddy who is big into psychedelics, not an abuser if you consider once monthly planned trips, not an abuse. He's working on modeling the things he's seen in CAD and these triangles are among those things.
Yea you see them often when you take LSD. Or at least I would when I was younger. I'm too old to further that experiment any longer but I'm glad someone still is.
@@acmhfmggruidk crackheads be using crack everyday not once a month
@@acmhfmggru
Once a month is not considered addictive behavior. Psychedelics can change the way we perceive the world around us and has helped many people. Plenty of studies to be found that back up that argument.
@nickwest932 Most people shouldn't be taking psychedelics without necessary guidance from a professional. The experience can break people and it does happen to some. There's a lot of work involved in integrating the experience.
@the11382
Still, to consider once a month as addicted is a bit much.
"Maybe it only affects the bacterium in certain conditions."
That was my thought too. That fractal packing might offer certain resistences against infections or environmental influences. Things like these usually come into wide spread existence when the majority of a population is wiped out with exception for this particular variation.
It’s NOT a fractal. It just vaguely resembles a serpinsky triangle if you just look atva triangle with an upside down triangle inscribed inside. Kinda like the way kim kardashian vaguely resembles lizzo if you just look at them from behind.
Your wrong but ok
@@joooood233 I’m right since you clearly don’t know what a fractal is and/or didn’t watch the video. A life learned on thumbnails and headlines…
Didn't I see this in The Andromeda Strain?
Everybody saying tri-force,
but I'm thinking metroid
1) it’s not a fractal. It just assembles into a particular shape
2) it’s difficult to assess fitness value of a particular sequence in the lab. The challenges and stressors encountered in the natural environment are difficult to predict
Exactly, this is basically a crystal.
@@jairo8746No it isn’t. If crystal structure was all that was needed to explain this then it would just be a solid triangle, but this one has spaces in it.
It does display a sort of “fractal” structure in a way. The base structure is 3 molecules forming a triangle. 3 of these base triangles attach at the ends and form a larger triangle that has a space in the middle, a space that appears to be 1 molecule in size. This 2nd larger triangle can be tripled to then also form a 3rd larger triangle with much more space in the middle (this space seems to be 6 molecules in size).
If it was just an isotropic crystal, the large triangle that is pictured would have 36 molecules, but instead it has 27. That being said, repeating crystal structures can be very complicated (such as in the case of micas), so what if the base structure of the crystal is actually the 2nd triangle? That still makes it so the final triangle has 30 molecules instead of 36.
Based on my limited knowledge of chemical bonds it appears as though the ends of the large triangle would still be wanting of some sort of bond to balance them, so perhaps this pattern can continue indefinitely. Given the limited information that can be gleaned from the images, there is a sort of fractal nature to this that can’t be explained by simply citing crystals, but there are only 3 iterations of this “fractal”, so there’s nothing here to say that this pattern continues besides the above assumption.
You say "it just assembles"...but that leads to the question "why?". Is there some possible explanation rather than saying "it just does it"? Maybe not, but many fractals can be seen as an attracting structure of a simple dynamical system. In particular, the Sierpinski triangle is the attractor of a dynamical system consisting of (1) shrinking in size by a factor of 1/2 and (2) three appropriate displacements in space. It might not be the case but it seems at least possible that the triangular shape might give some insight into the "forces" that create that particular shape.
@@dmytryk7887 protein complexes can assemble in a lot of shapes. By the way, an entire organism is build up essentially because of proteins being expressed and assembled according to space and time coordinates. To create a brain is no small feat.
You don't know what the definition of fractal is do you?@@antoniopannuti2088
Fractals resonate, which minimizes energy. They're stable. Maybe resonance in the chemical sense doesn't apply here, but if it does, then it makes sense that sharing it over a larger area would be an optimized geometry for free energy reduction.
No accidents. No coincidences.All by design.All with a purpose and function. Perfection all aound us and within us. A lot we don't know. A lot we have forgotten.
no way, if this was any other channel I wouldn't believe. Pretty amazing!
Wisdom... Courage.. power..
you described why it would make hex-comb pattern, not the fractal triangle pattern.
Thank you again Anton!
Thanks Anton. Incredibly interesting!
3:50 "We have no ides how the ancients new about this." Mmm! 🤔
The ancients may not have known the mathematics of fractals but they certainly had the artistic talent for pattern making.
People tend to forget ancient peoples were just as smart as we are, they just didn't have the knowledge and information we do.
@@wynnnnnnn5227 Just as smart, but just as dumb too; intelligence correlates with access to knowledge and isn't exactly static, being developed with use. Modern people do have more access to information, so on average we should be more intelligent than people back then. Of course, that's on average.
@@leonardomarquesbellini"Intelligence correlates with access to knowledge" seems smug. Perhaps access to stimuli toward thinking, i.e., interesting data is a better metric. After all, so much of what we "know" is not true, and that doesn't make us more intelligent.
Knowledge is verified in its application for the solving of problems. The reason these fractals show up in ancient works is because you could build things with these patterns and they wouldn't fall down as you made them bigger
@@user-gv4cx7vz8t nothing smug about people now being more intelligent than people back then, and less intelligent than people will likely be in rhe future. It's just how things are, and how they should be.
Thanks Anton...excellent as always
Thanks Anton. It looks like a fractal at small scales but a triangular tessellation at larger scales.
Anton has been at the space & sci info biz for years. He's a champ in the field & only has 1.29 M. Sabine Hosenfelder is extremely tenacious, has often participated in high level international conferences, etc. & only has 1.27 M viewers. It is all to say that there's limited public interest in science & most folks would rather be lied to by MSM or be titillated with cats.
I always see fractals when using psychedelics.
Happens to me a lot too, not every time but almost.
All psychedelics are Schedule I controlled substances per Federal law.
40 yrs. ago, i noticed that the white designs found only on OVERO
Pinto/Paint Horses are fractal patterns also... God's an Artist!
Fractals reflect one of the most fundamental patterns of the universe, including our own psychology, and measurable electrical signals in our brains, heart, body etc
Yay!!! 🎉 The Sierpinski triangle is my favorite shape! I have a mural of them above my bed and I draw them when I get bored 😄
Andromeda Strain
It’s like putting spherical magnets together in that pattern.
This is very very cool !!
Excellent! Thank you so much for sharing it! 🙏🏼🌷
In the case of life, if you are going to build a large organized structure out of small uniform blocks using random mechanics, then fractal geometry makes sense because it allows that to happen in a natural manner.
It's more like a crystal than a true fractal. A fractal provides the same level of detail not matter what the "zoom factor". This cluster of proteins doesn't do that.
a crystal is a great example of a fractal....
It's a simple fractal, triangles within triangles (potentially within triangles etc. etc.)
There can be no true fractals in the physical world. The Universe as we know it is discrete, not continuous. So the hard limit to the smallest scale geometry can physically exist is the Planck length.
The problem is basically our zoom machines though
@@6ixpool520 Anton does also mention that these structures are likely formed by imperfections which causes them to be shaped around the void, hence the fractal. Perhaps the cause of the shape doesn't lie in the physical world?
Wonderful as always Anton. Thank you. 👍😉
I work with "floretions", a group in the mathemati sense, and know they are connected with an interesting algorithm allowing them to be represented by equilateral triangles. I was already on the lookout for this in nature so this is very cool to see.
One of the key features producing mathematical fractals like the Sierpinski triangle is the scale invariance of the forcing action on an otherwise random generator. That such a scale invariance would persist over at least three orders of magnitude like would be required here is very impressive indeed.
I love what you do on your channel,all of it
The shape shown at 3:34 is actually not the famous Sierpiński Triangle. Sierpiński Triangle has filled areas and voids of different sizes arranged in a particular way, which for it to be a fractal, has to repeat infinitely in all scales. Instead we have a regular arrangement in a hexagonal grid, which repeats itself in two dimensions, but not in multiple scales, so it's not even a fractal arrangement in the first place. It's more like a usual crystal lattice, but in 2D. Somewhat like graphene, but in this case it's not single atoms arranged in a hexagonal grid, but much larger units built from whole enzyme proteins.
Thanks again, Anton. Cheers from the Pacific West Coast of Canada.
The Andromeda strain
I understand that cell phone technology took a leap forward when fractal shaped antennas were implemented .
Something something efficiency?? 🤔
Sierpinski's triangle have a very curious feat. As it gets more and more triangle holes its perimeter tends to positive infinity in the same time the area tends to negative infinity.
So the reason scientists are moving away from calling it the "citric acid cycle" is because at physiological pH levels it is simply not an acidic process.
Cool. Thanks for sharing.
😊 Exciting that we can see such teensy-weensyness!
There's this super cool method of scanning tiny stuff where they bounce a microscopic needle off of a sample a bunch of times, and then measure how it bounces on different parts. They can then use that data to make a visualization.
Thats what my girlfriend said after seeing my penis for the first time :(
Oh this is so cool, serpinski gaskets in yeast! I knew that fractals are everywhere, but to find such flagrant evidence that they pop up in such fundamental life forms is rather overwhelming; Beautiful, simply beautiful!
Fascinating discoveries, exciting presentation, thanks 👍🤗
That looks a lot like the micophotograph of the organism in "The Andromida Strain".
Andromeda Strain? 😆
Merkabah - Vehicle of Light/Energy..
I believe our Ancient Ancestors knew far more than we will admit.
One day I hit my head pretty hard, when I woke up I was seeing these lines creating quite cool patterns all over anything that was 3d, turns out I was seeing the fractals, after this, I can say with certain that a circle doesn't exist, everything is made up of one shape and one shape only
All cauliflowers are fractals apparently, not just romanesque
I know you said "in such a way" which I don't really know specifically what you mean. But, the Sierpinski Triangle is on snail shells.
Courage, Power and Wisdom... They knew something....
it always makes sense, the multiverse is a fractal, thus so is everything inside (and "outside")
so are the penta and hexa grams .. congratulations, we've made yet another full loop and are approaching the center of time.
Dear Mr Petrov, i have 1000 utube subscriptions, yet your reports stand out as CONSISTENTLY interesting, entertaining. WOW! HOW DO U DO IT. My durtur (daughter) has learned SO MUCH just from your vids. So, THANK YOU
Shapes do love efficiency.
Hexagons are the bestagons for that very reason.
So fascinating! ❤
For anyone interested in fractals, look into the z axis of the Mandelbrot Set. It basically contains the equation for chaos theory.
Very interesting! 😊