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Why trees look like rivers and also blood vessels and also lightning…
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- čas přidán 4. 09. 2024
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Why do the same, self-repeating patterns appear in trees, rivers, lightning, and even inside our own bodies? Is there some secret, hidden rule of nature or mathematics that makes these intricate designs appear all over the place? Let’s talk about fractals.
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Fractals are cool.
Fractals are cool.
Fractals are cool.
Fr.
Fun fact: Fractals are being used to create realistic computer-generated landscapes and environments in video games and movies. Their self-similar patterns allow for efficient rendering and an infinite level of detail. They have really cool applications.
@@besmartFractals are cool
Fun fact: Fractals are sometimes used to create realistic computer-generated landscapes and environments in video games and movies. Their self-similar patterns allow for efficient rendering and an infinite level of detail. They have really cool applications.
Also in future, fractals may be used to improve cooling systems. As they provide infinite surface area in minimum volume, they can theoretically maximise the efficiency of transfer of heat.
Zelda trees
We know
Check out L-systems!
en.wikipedia.org/wiki/L-system
In real life, the phrase "repeated branching" is better, it's more accurate to the non-infinite nature of things(and the impossibility of a literal mathematical fractal).
Did somebody say Minecraft?
Unbelievable. I noticed this exact thing as a child, without a clue about fractals. My veins, lightning, and trees.
That’s called Fitrah
@@zara__xd i was about to comment "fitrah" haha
@@zara__xdcould you expand on the meaning? I googled it and I can see what the definitions are trying to say but I feel like there’s more to it that I’m not understanding.
X ZZ 8
@@TheResistance000 Fitrah is a feature or part of the human soul that predisposes every human to instinctively intuit a higher power (God) from the moment they are born, and this intuition can either be subdued or fostered based on a child's upbringing (i.e., how they are raised). This higher power is all-powerful, all-knowing, the most just, the most beautiful, the most subtle, the all-calculating, etc., and has created time and space in a way that reflects His attributes. Just like when a certain carpenter or artist has a signature style, the "style" of God's creation reflects His attributes.
So the TL;DR of why i wanted to comment fitrah is that, for Muslims, there is nothing in creation that is the way it is by accident. So when our lungs take in CO2 and produce O2 and water, and trees do the exact opposite, and they both look similar (aka the "fractal" thing in this video), they have been designed that way on purpose. And children, who have a very strong "fitrah"-an innate sense that "the sky looks beautiful because God made it" or "that leaf looks like a bee's wing, and a tree's branches, and lightning. that's so cool that they were all made like that"-are more likely to look at things like fractals and see them as signs pointing to their origin (being created by God to specifically look that way).
I ranted a bit, but I hope that helps somewhat!
Our exterior anatomy is fractal, too. Our arms and legs branch out from our trunk, which then branches out into fingers.
And then the little tentacles on the fingertips!
Wait, you have those, right?
@@siquod and the antennas on those tentacles. wait am i in the wrong dimention again dammit
🤯🤯
X ZZ 8
I think that's a "stretch" ... I'll see myself out.
My brain has formed fractal memories to efficiently learn about fractals.
study supersymmetry and apply that understanding to your own cognition, thank me in a decade or two when you start mastering what it truly means.... hint: buddhist monks have figured it out for centuries through buddhist cosmology.
@@metasamsara How do you apply supersymmetry to your own cognition? As far as I know, it is related to quantum mechanics.
@@metasamsara Most physicists don't even agree with SUSY, and there is no supporting evidence. In addition, multiple experiments failed to show that SUSY is true, also the Buddhists didn't know about fermion-boson spin correspondence theories, no one even knew anything about particle spin untill 1922, and was only understood later. Not to mention almost all of the things the theory claims to be linked didn't exist(bose-einstein and fermi-dirac statistics etc).
@@αβγδε nothing exists without its opposite, push, pull, left, right, up, down, front, back, relax, stress, etc, etc. valid for emotions and for nerve control and for thinking about physics in vectors☯ valid for conflict resolution, for power balance, for physical impacts, for gravity, for magnetism, for oh so many things. in fact, for everything that exists. To manifest you must define, to define you must exclude the rest. to exclude the rest you have to acknowledge it. light doesn't exist without darkness. Everything is like that, and supersymmetry works as a philosophy just as well as to explain quantum entanglement. and quantum mechanics are just what we call science that is ahead of the outdated theory of general relativity. everything is quantum. at every scale, in every context, of every substance or idea, all is quantum. quantum is the inability to simplify in order to explain. quantum is real time physics obeying supersymmetry and regulated by entropy.
@@metasamsaraYou cool if I copy this into a journal?
You know what else we see a lot in nature, especially on large scales? Spheres. Because a sphere is in every way the exact opposite of a fractal; the maximum amount of volume packed into the smallest surface area. All planets and stars are roughly spherical because no one point on the surface of a sphere is further from the center than any other point, so it's the most stable shape for something with a lot of gravity. Likewise, bubbles and water droplets are round because they have a surface tension that wants to hold the finite amount of material as close to itself as possible.
Well said!
Like spheres are holding everything in it (surface tension) while fractals are letting go, to gain bigger surface area. Which also reminds me of ying and yang.
That's poetic!
And to think that both opposites in that sense, fractals and spheres, have the same fundamental origin: Energy minimization.
@@carlosdoerner Fractals to collect, spheres to hold, both with minimal energy cost.
@@carlosdoerner🤯
A good analogy for Fractional Dimensionality is to crumple up a sheet of paper into a ball... the 3D ball is comprised of a 2D sheet with air gaps... it's 'D' lies somewhere between 2 and 3.
Self similarity is awesome... take a rough looking stone and hold it up infront of a far-off mountain and close one eye and their similarity is remarkable.
Good analogy!
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But is the sheet really 2-D?
my brain is vomiting, thank you 🙏🏾
@@JC-justchillin Technically, because of the 3d nature of the universe, absolutely not... but it's perfect for showing the concept.
The fact nature always comes up with the most ingenious solutions to problems is truly astounding. It feels me with a sense of wonder and awe.
hence more of them applied into modern human life through biomimicry, now! 🥺💚
Same here. Some of the simplest, most common-place things in nature can be literally awe-inspiring when you think about them a certain way.
cause nature is not just accident
It’s kinda funny how people denounce God but apply some of his attributes to nature being like ohhhh nature did this 🤡 mf who is nature 🤡
man the Benoit B.(Benoit B.(…) Mandelbrot)Mandelbrot joke is phenomenal
I legitimately did a golf clap at that one.
agreed, immediately texted four of my nerdiest friends and begged them to text the same joke to their four nerdiest friends. and so on
That slapped hard 😂
@@alecsyogacorner 😂😂😂😂
@@alecsyogacorner Friends?
I first noticed fractals when I took psilocybin mushrooms when I was younger, they were popping out everywhere. I've been obsessed ever since.
I noticed them just naturally when I was younger. I then tried mushrooms and it just enhanced it and I’ve been obsessed with these curious observations as well as others. Just opens up many more questions…
given that it neatly explains nearly all of these natural fractals, it seems odd to not talk about the fact that they all just follow the path of least resistance? as a kid i remember that the term “path of least resistance” allowed me to actually understand fractals in our world unlike explanations that just said that these systems somehow prefer maximum efficiency
That's really interesting. That could be
"path of least resistance = preference of maximum efficiency".
Maybe just a linguistic trick, but, we process things through our own filters. Thanks!
And least competition
Constructal Theory is a branch of engineering that does this. The idea is to mathematically play off two competing requirements in a system to find the optimum solution. The cost to make more wood in a tree is played off against the increase in leaf surface area for example. Where it gets really interesting is that it can also be used to predict the transition of a flow to turbulence, based on energy minimisation, without any need to model the fluid in detail at all.
Any system with 2 ways of achieving some requirement, one being quick but expensive and the other being slow but cheap can be modeled this way. A classic example is heat sinking, where for example expensive but more conductive copper and cheaper but less conductive aluminium are used together. The optimum solution creates branched geometries without any guidance but the properties of the materials.
that's basically what he said but he used the word efficiency, because it has to be efficient too in order to last, not just the easiest path. as someone else said, mostly a linguistic detail.
@genesises it's a linguistic detail that matters because it implies different concepts. Saying something "makes it's self the most efficient" makes it seem like it is self governing, conscious, or something is instructing it. In reality, it simply grows towards the path that is easiest to travel. Much like a river travelling down a valley.
Chaos Theory (the mathematics behind fractals) was my favourite module at university, and I've loved fractals ever since. That was over 30 years ago!
chaos is a concept with no relation to reality because 'order' and 'chaos' are just concepts in a relative universe
@@Purwapada chaos theory has real world applications though. it describes systems that are very sensitive to initial conditions like the weather, double pendulums, and many others. In fact, it was developed by meteorologist/mathematician Edward Lorenz.
@@joseville im writing my thesis about this rn :D
Can we relate this phenomenon of fractals in nature to entropy?
Unbelievable. I noticed this exact thing as a child, without a clue about fractals. My veins, lightning, and trees.
Even the fungal network on the bark follows the same patterns 🍄
fungus among us?
X ZZ 8
I've always wondered why asphalt roads crack in the branching shape. I didn't start this video expecting an answer to that question but I'm so pleased I got one!
And hitting a window just hard enough for it to spiderweb i now realize its energy that the glass took in 😊😊😊
My power flurries through the air into the ground
My souls is spiraling in frozen fractals all around...
That was my first thought!
Let it go...
I thought you said “power furries” at first
@@nikkireigns 🤣
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this video scratches an itch that my brain has had for 30 years. thank you. :)
That's why they call me "ol' Lightning Veins"
Same here, accept its because i have a rare blood condition where my vessels burn internally. People say it looks like i got struck by lightning when it flares up 🤣😂😂😂😂
All jokes btw lmao
People call me a schmuck. 😢
Some people call me Maurice.
@@TitularHeroine Cause you speak of the pompatus of love?
what
I wrote my senior paper on fractals in nature. I love them!! It feels like you can find fractal dimensions everywhere, like country borders, lightning, and veins in leaves. They really the coolest thing possible.
I remember looking at a tree once and seeing the dendritic pattern and thinking if the whole thing were visible it’d probably look a lot like a neuron, then I read a bit about power laws but since I don’t know physics this video really summed it up for me pretty eloquently. Now I’ve just gotta know why different plants take on different leaf patterns!
I have trees in my brain
@@cryptidofthemarshes1680
Brain is trees
😂
My WAGuess is that when you look at something like how it competes against other plants/animals, and other details about how it takes in nutrients, from what heights its competeing to be optimal, and things like how much energy it takes to move the leaves, the answer will start to show up a bit.
So, in those particular cases, its patterns are more optimal than other plants that its competing with
Next Video idea:
Why some fruits,nuts and vegetables have similarities with our body organs, and eating them help the same organ they look like.👀
Isn't that awesome & true!
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Does eating beans help the Kidneys?
8
1:18 Stared at the same tree for 4 hours pondering every imaginable question possible after a handful of psily mushrooms....so yeah I would say I have lol
What an amazing Creator we have!
Indeed!!✝️📖🙏🏻❤️
Fractals are the natural method of energetic sophistication in the Universe, and they all serve the same purpose and rule:
To expose itself through contrast, as without contrast, there is no progression.
I mean, yes, energy gradients are the source of all things happening in the universe, but what the hell is "fractals are the natural method of energetic sophistication in the universe" supposed to mean?
@@NeovanGoth Fractals could be considered one of the most basic languages in the Universe, like binary code, it can infinity articulate itself on the micro and macro level in order to communicate information.
Today I learned there are dimensions in between whole number dimensions. I also learned that what we call "trees" can sometimes be more related to other plants that we don't call trees. Finally, I learned that you can increase the surface area of a shape by making fractals of that shape.
Thanks for the lesson!
Are there bald kiwifruits?
space filling fractals are really useful in nature
Love that you concluded with the word “systems”. My friend is in data analytics and he calls these “non-linear dynamic systems” and they show up absolutely everywhere there are healthy systems
Finally a video we can use when people compare our river basin maps to blood vessels or a cabbage :) Great work, and thanks for featuring our work!
I have been looking for this answer my whole life.
This has always fascinated me. Thank you for expanding and clarifying it! It took me a couple seconds to get the Mandelbrot middle initial joke, but yeah, I laughed.
I do not understand the mathematical facts about fractals, but I have always been fascinated by their beauty. Trees, rivers, the human body. We are all reflections of each other.
I remember my math professor went into a side rant about this on the whiteboard and left the whole class confused.
Thats unfortunate. Sounds like if they couldve done it with a bit more prep, that it wouldve made for a very interesting lecture.
Its always great when peoples interests match what theyre teaching
Honestly I think this channel is by far my favorite science channel on CZcams
Okay so that joke is actually really good. 😂😂 Took me a minute....
I've been left with more questions -- and that's so cool. Thank you, Joe!
Joe, I love your videos. You make the info so entertaining. Thanks you for that.
Awe❤ When I was little I called broccoli "Baby Trees"
They should mention how fractals are a large part of the psychedelic experience and are produced by nature. The trips often come with a sense of not being confined by our three dimensions and have been displayed in art around the world for ages
I’m surprised you didn’t spend more time discussing the mathematics behind fractals to include the golden number and spirals. Also, I think it’s false physics doesn’t play a part in these designs because everything is influenced by gravity, and the laws of physics and nature that help dictate the design of our existence based on our needs to survive. Things like evolution, time, and the need for efficiency as you said, play major roles as well. P.S. Love your work 🙏
there are no laws of physics. just observed regularities, which can only be understood as regular by comparing them to something else regular. Which is a fallacy and collapses in the face of induction
@@Purwapada something defines our universe. Physics exist. and our understanding of it is relative. That is all. The physics of the universe is very real. Dont get carried away with 'nothing has any meaning' level philosophy ...
@@andrew5744 physics does not exist, it is the logical application of a conceptual framework. Based in the supposition that phenomena have a true existence.
Why? Because, an existent is not born of an existent (because it already exists), an existent is not born of a non existent, a non existent does not come from an existent, and a non existent cannot come from an already non existent.
As such there can be no arising of a true existent.
@@Purwapada again ur getting carried away with philosophical mumbo jumbo. mathematics exist as if I have one of this and I have one of this, I now have 2. Mathematics exists in our universe. If I walk off a building on earth, I fall because of gravity. That is physics existing. Our gravity is a constant rate of acceleration pulling downwards which is why we walk on the ground. Consistent Forces act upon us. And We apply force to move. That is physics. Not in any way saying our physics are 100% correct. But physics and mathematics exists one way or another regardless of what philosophy u attempt to bring to the table. We presently live in this reality that has an existing system of math and physics.
@@Purwapada one very philosophical person could of course say physics doesn’t exist, time doesn’t exist, math doesn’t exist, and plague everyone with unhelpful questions like well how do we know anything exists? But the fact of the matter is you exist. So you must acknowledge what you exist with currently. If you want to say u don’t exist. Be my guest. Don’t go around talking it’s fact tho. Kinda like genders. U wanna identify as something. Go for it. Think what u want, but don’t push that bs depressing mindset upon others who can acknowledge we live in this reality, whether or not it’s a dream and we’re in a coma or we’re a simulation, we are here… so how could u sanely try to implement that as the norm upon others. U say “physics doesn’t exist” like it’s fact. No, that’s your philosophical rabbit hole. Like the piers Morgan clip where the dude is telling Morgan that he is a cisgendered male when no, the world doesn’t run off of your individual phrases you’re attempting to make up, Morgan identifies as a male period which was his point. We all have our own interpretations of reality. And I, as well as many others can appreciate this vast system of math and science that dictates our universe. To say physics doesn’t exist is to do deny said “framework.” Yes physics and time and math are man made concepts to understand the framework. If we didn’t call time anything. Time still ticks and goes on. But we do have our way of understanding said framework by calling it time. So time does exist. To an alien civilization they could call this framework we call time zoobadoobah. And zoobadoobah would exist because it’s their way of understanding and describing the existing framework. The “framework” exists and thus our way of interpretation which is physics, time, math exists, whatever argument u wanna get into.
This is like a caveman argument. It’s like oh, well friction with this wood and oxygen creates this warm bright source that emerges and that potential exists regardless of if they had words for it or not when cavemen discovered what we know as fire. But obviously to advance as humans, they did create words for it in their native languages. “Man make fire” so they call it fire. Thus Fire exists. And man also exists. You’re literally arguing about concepts not existing when concepts are just describing what exists. Cuz even if fire wasn’t called fire. What we know as fire still exists.
What I find fascinating is that no tree is exactly the same, but still look familiar, because they grow the same type of fractals. No matter how different every single tree is, we still see what kind of tree it is. Simple but amazing.
Fractals are so efficient and yet humans still prefer grids and squares :(
Thanks for your video! I met fractals in an event of the UBA in Buenos Aires. 5 People explaines their work investigating practical uses of fractals. Came out amazed. I have never forgotten that sensation.
Love the aspen tree reference.
That's pretty neat!
I’ve been waiting far too long to feel validated in my obsession with fractal patterns. Thank you
As a game developer, paying attention to this is how im able to create more realistic looking landscapes.
With landscapes, when reality breaks away from self similarity is also super interesting. Kenton Musgrave talked about that in Texturing and Modelling (I believe it was)
Then of course, mixing the 2 to get really great stuff is so much fun.
Wait until you discover Perlin noise. ;)
We are indeed made in His image
I'm a bioinformatician using fractals specifically to study viral evolution. Fractals are a really interesting way to study genetic information because by representing the information as a fractal - somehow you include information about the DNA sequence's physical structure! It's really exciting to work on it since little is understood, but I'll be doing my best to push my field forward! So that statement about "no gene causing fractal growth" might still turn out to be false!
The Awe of Gods creation 🙌🏽❤️
An episode on tree roots would be good! (They don't actually look like a mirror of the tree crown. They are pretty much in the top 3ish feet of soil and spread out like a plate. Even in "taproot" species)
I saw this really cool fractal while making a blended coffee running down the side of the cup. It was running like perfect branches/ snowflake style going down on the cup. Looked so COOL
I need a “I ❤️ fractals” shirt
I saw somehwere that trees roots don't actually grow like what most people have been lead to believe, they grow a lot more horizontal than vertical
I think that is very dependent on the species. Some are evolved to create a shallow communal "root mat", but some depend on "tap roots" to dig deep for water.
Clear explanations what are fractals. THANK YOU !
Aww dang, I’d been chatting to Matt Parker about doing a collab on this exact topic. Awesome job!
Those "rules" are the force of consciousness, a field of directions, like an instruction manual! It's so beautiful.
These words have no meaning.
Your videos always leave me feeling inspired. Just wanted to say that.
I wish this man was my science teacher back in hs. I’ve learned so much in a few minutes and was hooked on watching. Great job PBS 🎉
What fascinates me is that the big tree in my parents' backyard survived a lightning strike but only half of it did. The other half is clearly dead and it is a split right down the middle. It isn't obvious from looking at it that lightning did it, but I was watching the storm from my bedroom when the lightning strike hit. It shook my windows it was so loud. How does a tree survive that amount of energy?
And related, why do people get those fractal-shapes when receiving strong electric shocks?
I love fractsls, drawing trees and seing them everywhere is beautiful
A more than wonderful episode, but it must be pointed out that living and non-living systems do not have any free will, but rather natural fractal patterns are subject to physical laws and principles purely without any intention, and this is what drives us to understand the nature of...
This is true. You baiting?
@@borttorbbq2556 what is the meaning of "baiting"?
Emergence can explain free-will and intention, we can't explain emergence using only the scientific fact of uncontrollably(regardless of the deterministically vs. randomality of quantum mechanics)
@@uasserkamal2002 Basically, you say something you know will piss people to get people to reply. It kinda forces interactions. I do it often. In this case you're saying the quiet part.
@@spoperty4940 hmmm explain that to the experiments involving this. Your brain makes the decision even if "you" are thinking it over.
Conversations are also like branches/ fractals, they branch off into unexpected directions
Everything is connected 🌳
Transportation infrastructure also has fractal branching, from the smallest dirt roads across a farm to the largest highways across a continent.
Wanna know something freaky? Your hands are fractals. Each of your fingers is just a tiny arm where the outermost knuckle is a wrist, the middle an elbow, and the innermost a shoulder
I can’t unsee it now…
Oh man
Mind blown.
it made me think that the human body itself looks like a weird stylized hand too, like a biped like seastar
That scene in Ghost und the Shell where tiny mechanical fingers come out of a hacker's fingers. :D
Awesome vid! Fractals could be found in man-made architectures - road network, telecom network, social network etc.
You call them fractals...and i called it the Signature and evidences of the divine being
I noticed in Google Maps, the distribution of small towns and the roads connecting them looks just like neurons.
Especially in areas towns are 5 miles apart or so to allow people to walk between towns before cars. If you find a place without a lot of other clutter like forests, you can see it very clearly.
Anyone interested in fractal branching patterns and how they relate to flow systems might benefit from checking out the book Design In Nature by Adrian Bejan.
The world will be a better place when the top trending YT videos everywhere will be premium science videos like this one. ( Also when scientists are mainstream celebrities ; not actors, not influencers )
Have you ever heard: as above, so below? It just says that certain things mirror themselves.
5:54
It was probably easier to evolve that pattern (grow, split repeat) that to have gigantic leaves and branches (if a herbivore eats it's base you have to regrow the hole thing).
life is a doctor who episode, that's why
This is underrated
And it’s only 3 minutes old
*insert 12th ranting*
I truly cannot believe that your video is titled like this. I taught a class of drawing to my students. We were drawing plants and I mentioned how similar blood vessels look to branches. Then this week I looked at the trees here in winter and thought abt how amazing it is. Seeing as trees are like lungs. Now I see this video. Its not the algorythm for once. Radical coincidence. Tx.
PBS / Nova - Fractals: (Hunting the Hidden Dimension) czcams.com/video/qABFYiYqXSU/video.html
Has always, I always think this topic won’t interest me and then I’m hooked for an another episode
I miss when the channel was named "It's Okay To Be Smart". I dislike the simplification of names and app icons that's been trending.
This and the clikcbaity titles on this one and related channels lately. I get its for the algorithm, but still.
And the hello smart people...😢
We have designer, a creator. God created everything as His masterpiece.
Amazing video. Wish you mentioned human greated ones. Like the electoral grid or mainly the road system. Going from motorway to main road to street road. I use this to great effect in city building games
God is amazing.
We need more fractal studies. Fractal operations hold the key to a new way of energy development
The underground part of a tree doesn't look like the top part. They used to think it did but now they know the Roots spread out and remain relatively near the surface .
Depends on the species. A lot of desert plants have roots systems that are way bigger than their part above the ground and vice versa for a lot of tropical species. But I agree, you can't generalize them as such, but that's exactly the same for your comment as well. 🙂
the point made isn't that they look identical - noone "used to think this". you'd be pretty special to believe there were branches and leaves identical, but underground - and maybe equally special to make this into some kind of argument lol.
the point is that the fractal pattern is the same.
@@BackYardScience2000 well yes but, obviously, here he is referring to averagw trees in fairly 'normal' temperate environments. The kind of trees you see around your house when you go outside. I don't think he is referring to any exotic desert growing plants.
@@genesiseswww.yourleaf.org/blog/brenna-anstett/sep-18-2014/mythbusters-getting-root-it
Love this! Thanks so much! Once you see fractals they find you in everything, they cannot be unseen in my life. Great video 😊🪷🌾🕊🏝🌲🌳
God is good ❤
i love it when nature min-max things with geometry like with hexagons and fractals
Fun fact God created everything..
Once I got really high and said "trees are reverse lightning" and I've thought about it every day since
Thank you! Now I sleep while seeing fractals haunting my dreams because of my ceilings.
NEW BE SMART VIDEO DROPPED THIS BOUTTA BE FIRE 🔥🔥🔥🔥🔥🔥
What a good speaker you are! My first time at your channel - you're a natural in front of the camera.
this is the coolest video I have ever watched in my entire life
I looked just in time to catch the neature walk reference. how neat!
As a math guy u were tickling my brain in the middle 3rd of the video.
Essentially we're trying to maximize surface area to volume without over/under commiting resources.
In a sense they're anti-bubbles (or balloons in the context of lungs, blood)
Well said!
Definitely cool how the inside of certain fruits and things looks like the magnetic field. Amazing how nature forms its masterpiece’s .
Fun fact: trees root systems mostly don’t mirror the tree, instead they branch just a few feet down far shallower than we were all taught
Joe’s hair be looking HELLA fresh my man
i love your videos. you cover so many random topics which all are so damn interesting. you really feed my inner nerd so much interesting information.
Now that i think of it, we are kinda fractal-like too… Torso → arms → fingers…
I seen fractals when I was on magic mushrooms, it looked like vibrating strings of light (search up the “Paisley” Pattern) on a bandana. When I looked closely at grass- every single blade of grass was growing into this ‘energetic pattern.
My brain is fractured now.
As the video progressed, it felt calming and so soothing. As if life is good now and everything seems beautiful. Saved this video to watch again. Thank you for teaching us cool science stuff Joe❤
Did anyone else used to draw fractals as a kid in class? I had triforces everywhere at one point. Seeing this video was like scratching that itch I had as a kid drawing those.
Merry Fracmass
WAKE UP BABE ANOTHER HIGH QUALITY FRACTAL VIDEO JUST DROPPED