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My (stupid because it is not as general as it sounds) reason for "why the nature likes fractals?" is that: It is a way of "breaking" the surface to volume scaling problem.
Because cells are literally cellular automatas like things, that use genes as programation. The repetition comes from the nature of cell itself that replicates.
I believe fractals allow an interface with entropy, life is a meta-stable process of lower entropy particles that has to maintain that (homeostasis). Does that make sense? Life arises from the interface of entropy, the greater that “surface area”, the more complexity and ability for it to function. That’s what I have been theorizing
@@BoxOfCurryos well, I was thinking about lungs and oxigen capure for example. If your lungs where just like bags and not fractals (with traquea and brochi and bronchioli .... ) then surface for oxigen to enter the blood stream would grow with L² ( L a characteristic length of the animal). However, the amount of oxigen needed grows with L³ ( proportional to the mass of the animal), and hence, having bag like lungs is less and less efficient with the size of the animal. However, the surface of a fractal grows faster than L² (indeed it can even grow as fast as L³) hence allowing very big mammals to have lungs quite similar (in proportion) to small mammals.
Fractals in nature follow much simpler rules sets based on bifurcation and boundary acknowledgement. It’s that simple. Some organisms favor spiraling rule sets in place of the bifurcation L-system approach, but the boundary acknowledgment is more or less universal as it is optimal for survival or greatest potential for occupying the greatest surface area.
Explain why this is also in engineering? Just one of my questions… why does most things in life resemble fractals? e.g. brain circuitry, to even mathematical map of physics such as light, sound, etc, all mesh together to make a result, one symptom being the result of an architecture topology of fractal geometry, roots and trunks. this is a philosophical question, so is this just a human made algorithm to make things more easier to comprehend e.g. math, or is this actually prevalent in our life? this isn't just prevalent in nature, it's also prevalent in complex engineering systems especially electrical engineering in computer systems or power systems. something tells me that all this is the collateral result of logic circuitry. even chemical or physics, what we can visually comprehend is just the tip of the iceberg whilst there'd be fractals if we could map it out. should we infer that it's always associated with logic circuitry or networks
@@BritishEngineer This logic system is the origin of reality, and the best method we have to explain it. Beginning with the evolution of dimensional space, from one to two dimensions, then from 2 to 3 Dimensions; The principle of expanding perpendicular to your previous trajectory while acknowledging previous and future evolved paths is what creates this non-intercepting growth pattern. It requires elementary logic and consciousness.
@@Cardioid2035the interesting thing though is, if god is an intelligent being that has mental processes and can make decisions, then the mathematical ‘superstructure’ precedes him/it rather than coming after it, since intelligent decisions require mathematics for values and quantities and requires logic to make decisions based on information. Very interesting stuff
@@BritishEngineerMaybe I have the answer. It is the nature of reality to communicate itself to us. It is the nature of nature to express itself. The phenomena you are witnessing is reality communicating it's very nature to us. Fractals aren't the only thing it's screaming in our faces. What a world.
What’s of most interest to me is how fractals relate to the psychedelic experience and ultimately how we likely view and process the world. Humans are great at recognizing patterns and ingesting certain psychedelics increase that by a substantial amount, to the point that seeing fractals in objects or simply overlayed on top your vision is a widely experienced effect. What I want to know is what in the human brain causes us to see (what appears to be) mathematically accurate fractals while under the influence of psychedelics. I have personally seen perfect Sierpiński triangles in incredible detail, among other types of fractals
Personally I think it has something to do with whatever underlying math our brain always has going on in order to recognize patterns. Some people in the comments think that fractals are maybe some kind of fundamental or underlying function of the universe- which would be interesting, especially if taking psychedelics “reveals” that fundamental aspect. I don’t think there’s anything special about it personally though, it’s likely just a side effect of increased the pattern recognition and nothing more
This is what I've been wondering too!! Took the words right out of my mouth. Also agree with your theory that it may have something to do with the brain's mechanism for pattern recognition...but would be cool if we knew more about this.
Think about dynamic programming: we can break down a problem into overlapping subproblems (we can repeat the same solution recursively), and optimal substructure (maximizing surface to volume). Nature figured out dynamic programming and its solution is fractals.
Does this mean that DNA is not only Turing complete, but also can be translated to a higher level programming language? Never thought of biology from the CS perspective. Can we program an operating system instructions to a DNA code? Would that be readable? So many questions. Thank you for this video, I feel like I've found a new interest.
It is simpler than that. If you iterate any rule system you have a fractal. Fractals are simply the emergence of iteration. Doesn't matter what the rule set is except that some rules will degenerate into things we do not call fractals. The world is "fractal" because it is recursive/iterative. Cells divide(that is iteration). Atoms range themselves according to atomic rules which then create emergent patterns which are fractals. It is because the universe is a differential system and all differential systems are fractal(again, they might degenerate). There really is no other way to do it. How else do you get complex systems without building them up? We know from experience that things just don't magically appear in to existence. Things are build up through "work". Anything that is built up from other things will be a fractal expression of that thing. Either one gets a fractal system that works or one that doesn't(it will not function in the world). It's just evolution at work and evolution is just a time dependent different manifold. Differentiability ensures things progress in a "sustainable way". What people should be asking is why is "God" a mathematician. (the obvious answer is he is not but that mathematicians are "god"(or at least can speak his language to some degree)). If one understands differential growth and the implications of that along with the sheer number of "experiments" that go on, it is obvious how life works. It can't work any other way except to die out and then not exist(but if it did we couldn't be here). Surely there is a more complex "algorithm" than differential iteration(E.g., Eulers Algorithm) being used... but it is unlikely that the "actual algorithm" could ever be expressed in man's mathematical language. Regardless, approximations are valid. If you have rules of a system and allow those rules to interact and propagate in a smooth way you will express the complexity of that system. If the rules are consistent and complete you will get infinite expression. The rules for the universe are almost surely consistent(although maybe not but we could say they are at least empirically consistent) and they seem to be complex enough to give completeness. It's really not that much more complex than this. It's quite simple in fact as long as you don't need to know every little detail. E.g., a chess game has +10^50 possible games but by knowing the rules of the game and how to increment it you can learn how the game expresses itself more or less, on average, quite well. You don't have to know all possible games because most games are nearly the same or express the same ideas. Same with life. Variations on a theme...
@@littlehuman7028 A differential dynamical system. "Life" progresses by "step" and feeds back in to itself(today depends on yesterday, the now depends on what happened a femto-second later). Because of this, the "equations of the universe" whatever they are recursive: Present = f(Past) And hence Future = f(Present) = f(f(Past)). The point is that it is a recursive system. It is exactly analogous to a dynamical system. It is recursive. Recursion itself has properties. That is, all things that are built on recursion will have certain abstract things in common because of the recursion itself. Because "today depends on yesterday" there are certain fundamental constraints that are necessary to make that true/work. That is recursion. The study of recursion then teaches one how life works in very general ways such as why life "looks" the way it does. Studying fractals helps one "see" the fractal universe and wrap their mind around how it is all put together. It also then helps to understand why life also seems to have chaos in it. Studying dynamical systems such as the logistics map helps one grasp such concepts. Essentially because life is a differential system by studying differential systems one learns a language that helps one understand life itself. You realize that what happens in life is all according to certain rules and you can see how those rules play out. Even if you cannot wrap your mind around all the information you can still see the general patterns. This is what people are currently doing and as more people study such things the knowledge contained within them will become more common(obviously). It is not something that can be easily explained and a person will only understand after spending a large amount of time studying the mathematics of such systems. The more they study the more they will understand. Of course it isn't just studying math but also life such as learning history or learning biology, etc. You will learn "it can't be any other way". Life may not be entirely a differential system but it mostly is and hence studying the mathematics of such systems will teach you a great deal about life. You will also then realize that most of what people talk about when they are talking about meaningful things in the world are actually related to such systems and how they work. It won't give all the answers but it gives a solid foundation to build off of. When studying the mathematical systems that are examples you should always work to see more complexity in them. The Mandelbrot fractal, for example, may or may not be found in nature, but seeing it as a representative of complexity and how iteration creates it helps one see how iteration creates complexity in real life. A very good way to see this is video games. They are recursive systems and they generate worlds. They are a good model because one can pretend the universe is just a video game world generated by some "algorithm"/"program"(which a lot of people fall in to the trap of taking it literally and say things like "The universe is a simulation"). Understanding Emergence is very important too because it helps one get a handle on complexity. Most things we see at our scale are due to emergent properties and it can be quite confusing to people to connect them to the microscopic. This leads to a lot of false beliefs about how the world works. As time goes on more people will understand these concepts and it will bring more understanding(e.g., it is recursive) and this will open up how people think about the universe and all things in it including humanity itself and all the things it does. Humans are extremely recursive creatures(it is as if we work along the boundary between chaos and order). When we build things those things become stepping stones(iterations) in to future things which are built off of. All that is a recursive process but we have some control over it. Again, really one has to spend many years studying these things and over time it all just starts to make sense. There is a very good book that goes in to a lot of the mathematical concepts called "Chaos and Fractals".
Well put. It makes sense simply because life has to grow and replicate. To grow, you need a base organism that can live on its own, and then add to that. Fractals are the best way to do that. Because you can just keep repeating what's already there, to grow. Unlike something man-made like a chair, or tool, you can't grow it by adding to it - you have to simply make a new item that's bigger, from scratch. But nature can't just make a fully-functioning organism that's fully-grown from scratch. And yes, there's man-made examples of fractals too - you could expand on a room by adding more rooms to make a house, then more houses to make a hotel. But the starting room is still technically livable! That's the key. With fractals, the smallest instance is just as functional as the larger whole.
Amazing work. Please keep going. I would also like it if u include more resources for someone who wants to learn more about the intersection between mathematics and biology. I still have a lot of gaps in my knowledge.
“Fun” fact: Hilbert Curves are a type of Space-FILLING curve - so in essence - you literally are reaching ALL of the pixels on the image through the curve, the curve “fills” the whole 2D space. It’s not just “the majority”, it is in fact all of them. Also, probably worth looking up 3Blue1Brown’s video on Hilbert Curves, they’re like, incredible seriously.
The thing missing in the basic recursive definition is the execution environment. To even be able to create those recursive structures requires a computer (or person) to evaluate the state changes. Computers also require error free execution otherwise your result will have those errors compounded. This is just another way to say that the execution context is missing in the conversation about "algorithmic complexity" and the resistance to errors is important in biological systems.
I’m at a point of needing that elephant in the room addressed properly as well. It seems we only ever just kick the ontological can further down the road…
7:29. It's cool to think that you could fill this shape with paint and not have enough to paint it. Like I can't imagine a paint bucket that doesn't have enough capacity to paint even itself, assuming Infatesmally thin walls. But it exists and there's plenty (in theory). I wonder what it means that since it only takes a finite ammount to fill it, we could hollow it out and have the same shape, but painted and negligably smaller. Like an infinite quantity minus an infinitesimal is finite. Just hurts my head to think about. Maybe an infinitesimal difference is negligible to us, but to an infinite quantity it is apparent. I love infinities
For a more intuitive example, with one less dimension, imagine the integral from 1 to infinity of 1/x^2 This curve is infinitely long and has an infinite length. But the area under the curve is finite, equalling 1. The reason this makes sense is because as the curve gets closer to the x-axis, the amount getting added to the area gets closer and closer to zero. Now imagine taking this curve and rotating it in 3d around the x-axis and you have the trumpet shape with infinite surface area and finite volume!
This is one of the channels that gave me the courage to start my RU-vid channel 8 months ago about self development. Now I have 1,126 subs and > 900 hours of watch time. I know it’s not comparable with others but I’m still proud I started because I’ve been learning so many lessons that I could haven’t learned without getting started in the 1st place.
Its very important to point out that the genes arent the primary instruction. They react in the contexts of dynamic chemical patterns and the genes are more like switches that are the result of the patternicity and not the origins. Embryonal symmetry is established chemically and electrically through the tissue intelligence and voltage gradients of the embryo itself and genes turn on and off in response to this
life forms get very complex... But simplex principle behind it is field-incommensurability: the fraction contains the information of the whole. The true holographic principle of selfOrganisation. This was the method of reasoning for infinite energy technologies(Open-system Electro-Dynamics); we live in a universe of infinite variety, which means we have infinite algorithm. Which means, by definition, we have infinite potential. ...
Fractal structures, especially in three dimensions, can be fantastically clever at bearing loads- minimum mass at maximum area. The largest structure in the universe follows the same principle because of the way that empty space expands much more than where the mass appears- the maximum usable (nonlethal) universe for minimum material.
Love the video, my only suggestion is add some more ambient background music for the rest of the videos, outside of the intro sequence, but that's just knit-picking. Thanks for your work, I look forward to seeing what else you can teach us. ;)
Small simple definition. As long as there is a fraction of an object, and that object fraction abstraction increases, or decreses deppending on which side you start to count, then you have fractals.
In the section at 4:51 the proper term is time complexity. The term "algorithmic complexity" is ambiguous and depending on the field can be either time complexity or minimum description length (ie length of code, not running time).
I mean fitting information about complex structures into small molecules i.e. DNA. Not sure if anything along these lines is proven yet so it may well be wrong.
thank you so much for this hight-quality content! I have been looking for a similar video about the occurrence of fractals in biology for a long time. This is a very beautiful explanation of the complex structure of the body, combined with the ability to adapt and quickly rebuild. Such content is very motivating, thank you again!))
Life is not fractal, it is constructal. It uses divide-and-conquer, just like many computer science algorithms. The main reason why these approximate fractals are ubiquitous is because they are close-to optimal.
Fascinating video. I truly find it amazing how incapable we are at describing any rational behind natural processes without almost anthropomorphizing it. Surely, nature does not use fractals because they are an efficient way of coding formulas for structure building. Instead, many countless iterations of structure building techniques must have been attempted, and life using this technique, by pure random chance at first, must have then wiped out, by supremacy of course, all other life forms on Earth. Makes it all sound. Just a little harder to digest, although of course there are other explanations for the use of fractals in nature.
I think fractals are like recursive function, and most of the bio mechanisms(like cells) commuicate wiith each other with hormones. so it represents like fractals.
Wonderful video, really makes you think. It seems just like the Mandelbrot set, where the dynamic system forces a particular structure just that here the system isn't a complex polynomial but a biological process with genes and environment as initial conditions, quite cool!
Hey nano just a quick hypothetical could it be human socializing itself is a self repeating fractal procedure and the way we interact is by judging whose mental model is similar to us ?
0:00 before watching, I´ll put my bet on this: Because it´s the most effective way of growing something. Thanks to its fractal nature, a lung can have an extremely large surface to pull oxygen from. A tree can have exponentially more leafs and blood vessels can get distributed most efficiently. Also such recursive operation rely on scaling, so the initial information needed to control the growth is just as small as a fractal formula as opposed to storing the amount of cells, an organism is made of each by each. That´s similar to instancing and proceduralizing in Computergraphics, where recursive operators called "solvers" just take the input of a previous frame and run the same exact operation again. A simple example of this would be reaction diffusion solvers, that create intricate structures very similar to fractal organics. One of those solvers, the "L-system" is actually basicly a treebranch generator which operates on a simple code-language, that helps defining the growth rules. Kind of reminscent of DNA. Now I gonna watch the video 🙂 1:25 Ah yes, The L-System. I guess, I was on the right track here 🙂
just looked back at this vid for the first time in a while and i am amazed at the growth in views! you sure know how to rizz the algorithm LOL keep going buddy! :) (it should be obvious to you from the pfp alone who this is, finally made an account so i could comment cwl ;) )
"Algebra is like sheet of music. The important thing isn’t can you read music, it’s can you hear it. Can you hear the music, Robert?" - Niels Bohr to J. Robert Oppenheimer, Oppenheimer (2023)
I haven't watched this yet, but I'm going to assume it's because cells divide into 2, which nessesitates 2 different orientations at some point. That and fractles have massive surface area which means better storage while keeping better nutrient/chemical tranport.
Aren't all species like a wired form of fractar in a sense? Like in evolution you can kind of see the branching. Also in the chance view, a pattern that repeats itself ( living beings or fractals ) it's more stable that something which doesn't
I guess i get it It's all because fractals can be generate by repeating the same pattern over and over again And that's the easiest way to code a lot of complexity into such randomly generated thing as DNA So that it has to generate a code for a simple pattern once, then just put that on repeat The fractals are complex structures made using simple rules And the law of nature is: from simplicity arises complexity PS: I wrote this before watching, just so you know
Very few are, you just notice them more because you heard that once and you expect it. More things in nature DON'T follow a fractal pattern than do. Like an insane amount of difference here.
While the information is interesting, I believe sometimes the pace of the video slides is too fast, one slide comes right after the first's animation just finished. I found it to be a bit annoying, but I concede that I usually tend to like slower paces. Hope this was good feedback.
Just one of my questions… why does most things in life resemble fractals? e.g. brain circuitry, to even mathematical map of physics such as light, sound, etc, all mesh together to make a result, one symptom being the result of an architecture topology of fractal geometry, roots and trunks. this is a philosophical question, so is this just a human made algorithm to make things more easier to comprehend e.g. math, or is this actually prevalent in our life? this isn't just prevalent in nature, it's also prevalent in complex engineering systems especially electrical engineering in computer systems or power systems. something tells me that all this is the collateral result of logic circuitry. even chemical or physics, what we can visually comprehend is just the tip of the iceberg whilst there'd be fractals if we could map it out. should we infer that it's always associated with logic circuitry or networks
What you call “imperfection” is, indeed, an imperfection for a mathematician, but is the very source of LIFE for a biologist. That’s the best (only?) definition of life: complexity-creating imperfection happening throughout while larger structures are self assembling themselves: particles - atoms - molecules - cells - organisms - (implemented) consciousness.
@@studiouskid1528 True, with the addition (disclaimer) that a certain phenomenon can have multiple valid explanations at the same time. Imperfection, for example, has a dual nature: it can simultaneously be considered a random error and intelligent instruction or internal message. I could model this with the double slit experience: if you measure it, the answer is particle, if you don’t measure it then it’s wave. Looks like you can decide for yourself: it’s up to you to measure or not:)
Ok but why does a fractal mathematical model exist as a default regarding our existence and not another? Who or what set up the framework to run the recursion formula to begin with?
Electric phenomena are fractal and scalable. Go check how plasma, which is filled by electric currents by its nature, mirrors differnt type of cells. DNA it s a great example as the shape of a coiled double spirals mirrors perfectly how arch lighting moves, like two snakes moving straight while coiling on each others. And ofc things like how lighting, rivers and trees all have the same type of fractal patterns. I wish there were more studies on the relationship of fractals in nature and electricity bc there is definitely a huge connection
I would like to think that electrons, and all particles, have their own fractal shape. So, maybe fractals begin are the very bottom, and that is why it is intrinsic in our universe...
The universe is an 11 dimensional, holographic, fractal. Its interesting how prime numbers manifest themselves in nature along with it's fractal expressions. its possible that sound wave shapes, through cymatics, my have fractal shapes as increases in frequency sees a positive correlation in increasing in complexity of the frequency. Something to consider.. 🤷
If that horn has infinite surface area bc the small part of horn goes to infinity then it does have infinite volume. It doesnt matter how tight and small the end is if it goes on forever right?
