The mandelbrot set was discovered as a result of research on the julia sets. The julia sets use the same iterative equation, but c is set to 0 and the set consists of all z where the iteration remains bounded. Interestingly, the julia sets and mandelbrot set, because of their shared foundation, are related; the mandelbrot set is the set of complex points where that z creates a julia set that is one piece. In fact, the mandelbrot set and the julia sets are merely the same fractal, but different projections of that 4 dimensional fractal into the second dimension.
@TheGhost How is the equation simple? How did he make that on his computer? Numbers didn't create an image the guy using the computer did! This video makes no sense!
You can understand it if you work at it! The rules for generating the Mandelbrot set are pretty well explained in this video. However, if you are unfamiliar with complex numbers, you will need to do some more reading about them and then practise doing maths with them. There is a small mistake in the video, though. He says that you should colour a point black if the complex number that it represents goes into a loop. He missed the possibility of a complex number not going off to infinity but also never going into a repeating loop. Even if the number does not go into a repeating loop, you should still colour it black, as long as it does not go off to infinity. And then you have the Mandelbrot set. :)
@@mattco1103 it is fairly simple to create: iterate over every pixel. for each pixel converte its y value to its complex number equal and for its x values converte that in is complex number equal as well. then While (some number < maxIterations && abs(complex number) < 2.0) then apply the equation z = z^2 +c; based on how big the some number is you assigned that to a rgb value. then after you looped through all the pixels you will have the Mandelbrot
I do find this very interesting, I do not believe in a human god... it's preposterous. I think what he means by seeing god in this scenario is seeing creation and life, and things we cannot describe or understand, so we call it god and that is what I agree with. This is my opinion. Great video man!
+Ganja Crumbs I agree too. In fact, let's exchange all unknown variables with the word "god" then we won't have to describe or understand anything ever again.
Wow. That’s how I feel. I honestly feel like I’ve seen this design when I took DMT. I saw a machine that worked in a way I didn’t think was possible. But now I see that in nature it’s absolutely possible.
Ever since I first found a video on a Mandelbrot zoom I’ve been fascinated by them. I always wondered how that man could come up with a mathematical equation like that. It makes me wonder...are there others like that? And what if there was an opposite? What would that look like?
to answer all of ur questions the formula z^2 + c is actually really simple there are other fractals, like burning ship, perpendicular mandelbrot & burning ship, tricorn, buffalo, celtic, other stuff (there are infinitely many fractals) there is an opposite to the mandelbrot set, the inverse mandelbrot set (z^2 + 1/c)
Nah. Ive been doing lsd + weed since my first time i tried lsd... No matter how hard my trip was I still able to see my friends, to see my sorrounding... I dont see no people on the fractals LOL wich leads me to say salvia instead due to ALL the fractals you see and how you arent able to even walk or talk hahahaha
@@andrewwoods4690 lol in that case yes. But imagine see you reallity mixed and messed(in the best way possible) by fractals then salvia +30x tripp is the way xD
I call it an argument where no one person leaves being wrong... Let's not forget shrooms guys. ALL of this type stuff is psychedelic in general, and no two people have the same experience with them, everyone knows that.
I experimented with this on my first computer in the early 80's. I saw the idea in Scientific American, (I think), and wrote a small program to crunch the numbers and plot it on the screen. As you can guess it ran damn slowly on an early 80's computer but it looked cool anyway.
@dannygjk - we share similar paths. I became obsessed after reading the Scientific American article and wrote a Fortran program to crunch the numbers and paint the pixels on an IBM XT. Took 4 hours to render a single image. Then I realized we had a Cray at Rockwell I could batch the calculations on the backend which took 1 second. Later on, someone developed FRACTINT which ran much faster on PCs by replacing real number calculations with much faster integer-based calculations.
Jimi Eisenstein -- thanks for authoring this excellent presentation. I appreciate how you describe that the Maldelbrot Set is in the complex plane which consists of orthogonal Real and Imaginary axes. Many (most?) videos I've seen gloss over this essential aspect, without which you can't understand how the Z^2+C function behaves, chaotically or otherwise. May I suggest a few additional details? I think they may bring even further clarity to this amazing mathematical phenomenon. 1. You mention that points within the Mandelbrot set such as (0,-1) "loop" between 2 previous values as they are iterated, such that Z5=Z3 and Z6=Z4. I believe that while this holds for a small subset of special cases, most points within the Mandelbrot Set "orbit" and converge towards a single value. For example, with C=(0, 0.63), Z spirals towards (-0.18, 0.46). (I acknowledge this can thought of as "looping"). Readers can setup an Excel spreadsheet to calculate a table of successive values of Z and use a X,Y Scatter chart to visualize this behavior for different values of C. 2. You described how different colors are used to indicate how fast Z grows. I think it helps to explain how "how fast" is determined and color assigned. After each iteration, the magnitude (square root of the sum of the squares of the Real and Imaginary components) of Z is calculated. Once it exceeds 2, we know the function will diverge (according to mathematical proof). So we note the number of iterations it takes for the magnitude of Z to exceed 2 and assign a color based on the number of iterations. So Blue may indicate those values of C for which it took 23 iterations for Z to exceed 2, Green may indicate the C's for 24 iterations, and so on. Solid bands of the same color indicate the same number of iterations for values of C in that region. The beautifully complex coloring just outside the boundary of the set arise from iterating thousands of times for each value of C in that area and assigning color accordingly. When the lightbulb goes off, you realize that all of the similarly colored points in an intricate filagree all take the same number of iterations to diverge, say 24,103 versus the neighboring points that may take 24,104 iterations. This is an elegant visualization of chaotic mathematical behavior that was difficult to envision before computing power made these numerical methods possible. 3. One last crazy thing about the Mandelbrot Set -- I believe that all values of C associated with a given number of iterations for Z to diverge are connected contiguously and enclose the Set in a single unbroken band. So if the color Red is only assigned to values of C that cause Z to diverge after 200,000 iterations, then the seemingly infinite regions of Red you find as you browse around are all interconnected in a single band. Thanks for indulging me in this long-winded tangent!
+Lee Cunningham and +Rogue Scholar.....You both seem to have a unique understanding of how this all works, so maybe you can answer a question that I have been wondering about. At the 3:30 mark of this video, another "BLACK" copy of the original comes into view, seemingly from among an area that is ALL color. It happens again at the 3:50 mark. Not sure how to ask this question other than in terms of the "FILL" function on most photo editors. If I was to "FILL" one of those black areas with a different color, would it also fill ALL the other black areas? What I mean to say is, are all black areas connected in some way, even if it's at a resolution where we can't see it? If not, can we understand what is different about these smaller copies, that they would just appear, isolated from the main copy for no obvious reason? I'm hoping someone can answer that question, because it's been bothering me since I first learned about the existence of fractals, and I'm definitely not smart enough to figure it out on my own. ….The reason it bothers me, is because I BELIEVE that the singularity at the center of black holes MIGHT behave the same way. I believe all singularities are linked together, even if it's by the tiniest possible pathway. .To be honest, it wouldn't surprise me if they were linked by a pathway that has no PHYSICAL size at all, but I have no idea how a person would go about proving that.
The Mandelbrot Set is like an incredibly complex and that seems so nebulous as to be useless, then it runs over you like a freight train and begins to make sense of the creation. A doctor tried to tell me how a intestine forms in an embryo and he used the term inside out but I couldn't get it. Jimi has done a outstanding job with this presentation. I go back to this when I get turned around or lost.
Say "God" and fedoras go flying. Anyhoo, the explanation in this video was great and I learned something from it. Fractals are awesome. They're in nature, too, like ferns or branches where the leaves repeat smaller and smaller. It's always fun to spot them.
It's been found that forests, themselves, are also fractal. As are structures in our bodies, and where the fractal begins to fail is the beginning of cancer!
So that's what it is. I've seen this before and wondered, what's the big deal? Someone made some designs and now he's just zooming endlessly. Sure, must have taken some work, but okay, big deal, you made designs and it's trippy. Little did I know, this has to do with math. Like wtf. This is so weird and seems like it has something to do with the structure of reality itself somehow. Reminds me of strange things like the phibonacci sequence (that has to be spelled wrong).
RUclips recommended a Mandelbrot video and I was going to comment what is it and why do ppl like it and this video was in the related section... PERFECT!
Actually he didnt choose the colors, the colors signify an integer value based on how far a number is from the value, each color representing a distance, "hot or cold" from the set
So, if you color every point that makes a loop in the mandelbrot equation black and every point that does not make a loop blue, where do all the other colours come from?
is not just blue. he stated that the numbers are colour coded base on *how fast the number grows* , not if it forms a loop or not. for example, a number that increases by 2 is colour coded red, while a number that increases by 0.18287373 is coulored cyan. so is a spectrum of colours
"...then we get this shape." *MANDELLYBROOT* *brain machine broke* ps: Whenever i see a video or something of a mandelbrot zooming in, i constantly feel paranoid. If anyone thinks im one weird b0i, im paranoid when i watch that because its like *falling through a void forever.*
Three things: α) AMAZING! β) super AMAZING!! γ) α+β!!! Everlasting journey from nowhere to nowhere. Somewhere in "between" we spend some time in existence. In my humble opinion is better to reconsider the next time we feel sad frustrated or everything with negativity inside, because is such a waste of precious time. By the way, this is a very good presentation of the true structure of cosmos. As we say in Greece, thousands of years now, Αεί ο Θεός ο Μέγας γεωμετρεί (Πλάτων- Plato for π=3.14...^ ), because everything, eventually, "end up" and "start with" numbers. Chris from Greece.
Agreed. And yet they also teach you a hypothisis that they claim is scientific law, even though it was debunked before the year 2000. ;) Here is a link to a site that barely scratches the surface on what is wrong with the Big Bang. In simple text. No "Scientific jargon" to make it sound smart. And it was done by Atheists, not "religious people" science.howstuffworks.com/dictionary/astronomy-terms/big-bang-theory7.htm
@@sparkylongtail309 Nobody calls the Big Bang a "scientific law". It is not a law but a hypothesis. It has not been "debunked". The early history of the universe is not fully understood, but as far as I am aware, all models of the early history of the universe involve a Big Bang of one sort or another. Nobody can come up with a better model that doesn't involve a Big Bang of some sort.
Alanish yeah all you need to know is that a square root of a minus number is imaginary, and anything that isn't a square root of a minus number is real.
@@artv.9989 Nope. And imaginary is the worst name ever chosen, because it makes it seem like imaginary Numbers are less valid than 'real' Numbers and they aren't.
but how the fuck am I supposed to have my guilt-free rape dungeon if god exists huh??? how the fuck am I supposed to do that???? THIS RUINS EVERYTHING *tips fedora*
Karan Lal Im an atheist but hol up a sec...just think about this. The big bang theory that states that everything came from nothing is just as ridiculus as saying that a higher power created the universe.
I understand it. Math is a logical creation, and consistent with itself. It is so simple a small child can understand, but so complex that it baffles the greatest minds of history.
KarmicYogi not only that but a great artist. Think of the sculptures of life he structured, the colors he painted (both seen and unseen) and the symphonies he composed (both heard and unheard). Amazing...
This is the best video for this topic. I didn’t understand and I frantically took to Google to find the answers but I was dumbstruck. This video cleared it up for me.
The comments on these sorts of videos seem to be divided between people who appreciate the knowledge and people who take drugs. I suspect that the intersection of that Venn diagram is pretty close to empty.
awesome :) Sad that people fear what they don't understand and will then blame you for it. I like your reference to God. It's an interesting analogy for an incomprehensible concept.
3:08 Most people argue about this being an "argument from ignorance" for God, but I'm more worried about you saying "no one designed this" and immediately followed with "God created this." What's up with that?
Recently, i have been seeing in my suggestions about some dude zooming into some kinda image, and I was like"What the hell?" Now i get it....Its much more complicated....😅🤔
I love it! It is one of my favorite Mathematical formulas. Why didn't they teach me this in Grade 4? They should teach this in Grade 4 to install a sense of wonder and love for Maths. It's so easy yet so complex in beauty.
Chill out, God haters. There is nothing wrong with finding and explaining the wonder in Creation. Your treatment of science as a religion is dangerous.
"God haters" I don't hate god, in fact I believe there _might_ be a possibility of a god, but there's no proof. Like a simulation. I just don't accept god being here because this just has to do with math.
We created the math, which is just a tool to formally define patterns and logic in nature. Math is a toolkit that allows us to see a lot more about the nature of reality than the naked eye does, and some things seem to work out so seamlessly it's not strange to believe in a concept like god. I understand the vision @CMC A holds because I used to used to be a full blown atheist, but there are in fact countless of metaphysical examples that can not be explained through science alone. Some things simply can not be expressed and have to be experienced. Try proving formally that beauty exists. You can't. There are limits to rational thinking, hence why our ancestors used countless of stories in the bible and other writings to make sense out of those things that can not be explained otherwise.
All science is simply an acknowledgement of what God has created and sustains. And science is constantly changing, whereas God never does. God and His Word are infallible, whereas man & his observations are not.
Friend. I am so greatful for your video inwhich you explained it very good. You covered many holes i had researching this mandelbrot subject. You got me closet to understanding. I only dont understand why : you pick random numbers and if the formula determines that the result is exponential results - then its not in the mandelbrot setup. You rlly explained it veryvery good, thanks. but plz explain it like i am 3 years old. You left some holes in the logic you were following. I rlly rlly rlly want to understand this. You rlly helped me!!
![Natanael Cano - Amor Eterno [Official Video]](http://i.ytimg.com/vi/EO4prCs6WpM/mqdefault.jpg)
Benoit B. Mandelbrot
the B. stands for
Benoit B. Mandelbrot
Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit Benoit ∞ Mandelbrot Mandelbrot
And that’s the point of Benoit B. Mandelbrot animations
They are infinite.
The most underrated comment on this entire platform.
seriously people sleepin on this comment. props to you this is clever as hell
the man himslef was a fractal
This makes me feel like everything is connected and everything is big yet so small
Which is the ultimate truth isnt it?
Dirk Gently would definitely agree!
- Kilo- this comment is why tesla is addicted to the number 369
Is your profile picture a picture of you shirtless smoking that’s not skinny
- Mikeg.lifts - it’s actually acid
dude you actually made me understand it
why do you say that? Zike
How? I'm even more confused now. This makes no sense
@@mattco1103 same
Not me
Fabian Johansson I’m too high to understand
Actually, the Mandlebrot Set has been nicknamed "The Thumbprint of God". Which shows just how much awe this shape inspires.
That’s fascinating
How does somebody even come up with something like this.
I can just imagine a teacher making their student create a copy of this as a punishment.
Easy. You just ask Matlab to create a colorcoded plot.
c++, done
#include
#include
using namespace std;
unsigned int maxrows = 100;
unsigned int maxcols = 200;
unsigned int maxiterations = 500;
int main() {
for (auto row = 0; row < maxrows; row++) {
for (auto col = 0; col < maxcols; col++) {
complex z = {0,0};
complex c = {(float)col*2/maxcols-1.5f,(float)row*2/maxrows-1};
int iterations = 0;
while(abs(z) < 2 && iterations < maxiterations) {
z = pow(z, 2) + c;
++iterations;
}
if (iterations == maxiterations) {
cout
@@JustinK0 yes but how is it just infinite, is it just generating constantly or is it something more conplex
@Olivia Leigh Yes, it would be a reward, not a punishment.
The mandelbrot set was discovered as a result of research on the julia sets. The julia sets use the same iterative equation, but c is set to 0 and the set consists of all z where the iteration remains bounded. Interestingly, the julia sets and mandelbrot set, because of their shared foundation, are related; the mandelbrot set is the set of complex points where that z creates a julia set that is one piece. In fact, the mandelbrot set and the julia sets are merely the same fractal, but different projections of that 4 dimensional fractal into the second dimension.
I don't understand why this subject doesn't get more attention. Something strange and very telling is happening here.
OpticSmurfable head canon.
It's called math morty might have heard of it 2+2=4
@MarzTek minus 1 is 3 quick maths
A Creator perhaps?
This is the shit I see when I close my eyes on an intense psilocybin trip
unfortunately I'm math stupid, but this is awesome as hell. don't understand it, but I don't need to understand to enjoy
That’s the key to life right there.
Don’t try to understand it’s unfathomable complexity. It’s not possible anyways. Just enjoy it :)
@@Zlaptheentity as they say, "ignorance is bliss"
@TheGhost How is the equation simple? How did he make that on his computer? Numbers didn't create an image the guy using the computer did! This video makes no sense!
You can understand it if you work at it! The rules for generating the Mandelbrot set are pretty well explained in this video. However, if you are unfamiliar with complex numbers, you will need to do some more reading about them and then practise doing maths with them.
There is a small mistake in the video, though. He says that you should colour a point black if the complex number that it represents goes into a loop. He missed the possibility of a complex number not going off to infinity but also never going into a repeating loop. Even if the number does not go into a repeating loop, you should still colour it black, as long as it does not go off to infinity.
And then you have the Mandelbrot set. :)
@@mattco1103 it is fairly simple to create: iterate over every pixel. for each pixel converte its y value to its complex number equal and for its x values converte that in is complex number equal as well. then While (some number < maxIterations && abs(complex number) < 2.0) then apply the equation z = z^2 +c; based on how big the some number is you assigned that to a rgb value. then after you looped through all the pixels you will have the Mandelbrot
"I see God" well that escalated quickly
Espen Sales how
I do find this very interesting, I do not believe in a human god... it's preposterous. I think what he means by seeing god in this scenario is seeing creation and life, and things we cannot describe or understand, so we call it god and that is what I agree with. This is my opinion. Great video man!
+Ganja Crumbs I agree too. In fact, let's exchange all unknown variables with the word "god" then we won't have to describe or understand anything ever again.
Ganja Crumbs the m
be gone, culture bot!
It’s like I totally understand it
But I’m completely lost at the same time
Wow. That’s how I feel. I honestly feel like I’ve seen this design when I took DMT. I saw a machine that worked in a way I didn’t think was possible. But now I see that in nature it’s absolutely possible.
Ever since I first found a video on a Mandelbrot zoom I’ve been fascinated by them. I always wondered how that man could come up with a mathematical equation like that. It makes me wonder...are there others like that? And what if there was an opposite? What would that look like?
there are many fractals like it, a lot of these recursive equations create fractals in the complex plane
to answer all of ur questions
the formula z^2 + c is actually really simple
there are other fractals, like burning ship, perpendicular mandelbrot & burning ship, tricorn, buffalo, celtic, other stuff (there are infinitely many fractals)
there is an opposite to the mandelbrot set, the inverse mandelbrot set (z^2 + 1/c)
The equation is simple, he probably came up with that just to figure out the solution and didnt imagine the solution would be so incredible
@@anotherfractalchannelisn’t tricorn the opposite of Mandelbrot set’s exponent
What if the universe is shaped like a Mandelbrot set?
Has anybody ever thought of that?
Last time i checked, the universe wasn't on a coordinate plane, making this exact setup unlikely.
I feel like this is my gender now.
T H R E E D M A N D E L B R O T S E T
Exactly, so we need to find the recursive function/fractal f(x,t) which creates self-aware creatures at f(earth,13billion years)
@@martinsleis3852 awesome😂
I have absolutely no idea how I got here or what this gentleman is talking about
i was on a geology homework video
How dare you
IBUMAX lmfao
Me to but I am gonna pretend I understand it anyway.
yo ni hablo ingles
I call it acid
No way. I'd call ot Salvia or DMT
Nah. Ive been doing lsd + weed since my first time i tried lsd... No matter how hard my trip was I still able to see my friends, to see my sorrounding... I dont see no people on the fractals LOL wich leads me to say salvia instead due to ALL the fractals you see and how you arent able to even walk or talk hahahaha
@@andrewwoods4690 lol in that case yes. But imagine see you reallity mixed and messed(in the best way possible) by fractals then salvia +30x tripp is the way xD
I call it an argument where no one person leaves being wrong... Let's not forget shrooms guys. ALL of this type stuff is psychedelic in general, and no two people have the same experience with them, everyone knows that.
Lsd
I experimented with this on my first computer in the early 80's. I saw the idea in Scientific American, (I think), and wrote a small program to crunch the numbers and plot it on the screen. As you can guess it ran damn slowly on an early 80's computer but it looked cool anyway.
@dannygjk - we share similar paths. I became obsessed after reading the Scientific American article and wrote a Fortran program to crunch the numbers and paint the pixels on an IBM XT. Took 4 hours to render a single image. Then I realized we had a Cray at Rockwell I could batch the calculations on the backend which took 1 second. Later on, someone developed FRACTINT which ran much faster on PCs by replacing real number calculations with much faster integer-based calculations.
If Pythagoras could see this...
Pythagoras be like: BUT WHERE ARE ZE TRIANGLES!!
Oh, no, they said they are against imaginary numbers, afaik
Pythagoras:
*what the cinnamon toast fuck is this*
Cult v2
Let's get it!
Ok, finding out this is naturally occouring just deflated my brain. Also youre an exellent teacher, keep it up!
I love the way such complexity can emerge from such a simple seed.
Jimi Eisenstein -- thanks for authoring this excellent presentation. I appreciate how you describe that the Maldelbrot Set is in the complex plane which consists of orthogonal Real and Imaginary axes. Many (most?) videos I've seen gloss over this essential aspect, without which you can't understand how the Z^2+C function behaves, chaotically or otherwise.
May I suggest a few additional details? I think they may bring even further clarity to this amazing mathematical phenomenon.
1. You mention that points within the Mandelbrot set such as (0,-1) "loop" between 2 previous values as they are iterated, such that Z5=Z3 and Z6=Z4. I believe that while this holds for a small subset of special cases, most points within the Mandelbrot Set "orbit" and converge towards a single value. For example, with C=(0, 0.63), Z spirals towards (-0.18, 0.46). (I acknowledge this can thought of as "looping"). Readers can setup an Excel spreadsheet to calculate a table of successive values of Z and use a X,Y Scatter chart to visualize this behavior for different values of C.
2. You described how different colors are used to indicate how fast Z grows. I think it helps to explain how "how fast" is determined and color assigned. After each iteration, the magnitude (square root of the sum of the squares of the Real and Imaginary components) of Z is calculated. Once it exceeds 2, we know the function will diverge (according to mathematical proof). So we note the number of iterations it takes for the magnitude of Z to exceed 2 and assign a color based on the number of iterations. So Blue may indicate those values of C for which it took 23 iterations for Z to exceed 2, Green may indicate the C's for 24 iterations, and so on. Solid bands of the same color indicate the same number of iterations for values of C in that region. The beautifully complex coloring just outside the boundary of the set arise from iterating thousands of times for each value of C in that area and assigning color accordingly. When the lightbulb goes off, you realize that all of the similarly colored points in an intricate filagree all take the same number of iterations to diverge, say 24,103 versus the neighboring points that may take 24,104 iterations. This is an elegant visualization of chaotic mathematical behavior that was difficult to envision before computing power made these numerical methods possible.
3. One last crazy thing about the Mandelbrot Set -- I believe that all values of C associated with a given number of iterations for Z to diverge are connected contiguously and enclose the Set in a single unbroken band. So if the color Red is only assigned to values of C that cause Z to diverge after 200,000 iterations, then the seemingly infinite regions of Red you find as you browse around are all interconnected in a single band.
Thanks for indulging me in this long-winded tangent!
Awe! I was just gonna say all that math stuff
Thx for further information Mr. Kunningham. (feel like im talking to my science professor.
Lee Cunningham you need a hobby
Daft Genius how about math thats a good hobby
+Lee Cunningham and +Rogue Scholar.....You both seem to have a unique understanding of how this all works, so maybe you can answer a question that I have been wondering about. At the 3:30 mark of this video, another "BLACK" copy of the original comes into view, seemingly from among an area that is ALL color. It happens again at the 3:50 mark. Not sure how to ask this question other than in terms of the "FILL" function on most photo editors. If I was to "FILL" one of those black areas with a different color, would it also fill ALL the other black areas? What I mean to say is, are all black areas connected in some way, even if it's at a resolution where we can't see it? If not, can we understand what is different about these smaller copies, that they would just appear, isolated from the main copy for no obvious reason?
I'm hoping someone can answer that question, because it's been bothering me since I first learned about the existence of fractals, and I'm definitely not smart enough to figure it out on my own. ….The reason it bothers me, is because I BELIEVE that the singularity at the center of black holes MIGHT behave the same way. I believe all singularities are linked together, even if it's by the tiniest possible pathway. .To be honest, it wouldn't surprise me if they were linked by a pathway that has no PHYSICAL size at all, but I have no idea how a person would go about proving that.
math teachers be like: WHAT IS THE PERIMETER OF THIS SHAPE
I know that’s a joke, but it’s actually something that can be calculated!
@@psykoj cant wait to solve that in math class
It's... imaginary.
Well the area is finite and can be estimated but don't bother with the perimeter
@@fruitchewx127 fixed
3:19 And now, we zoom in the *m a n d l e b u t t*
😂😂😂😂 same thought
Mandelbrot is dead, isn't that... wrong? Or did you mean Mandelbrot's Set?
It's called a Mandelbutt...
Mandelboob when
Mandelbutt
mmmmhhhhh recursive sets
hey i know you
SUCC
pija 18 cm
Luv u
Trigonometry 101
The Mandelbrot Set is like an incredibly complex and that seems so nebulous as to be useless, then it runs over you like a freight train and begins to make sense of the creation. A doctor tried to tell me how a intestine forms in an embryo and he used the term inside out but I couldn't get it. Jimi has done a outstanding job with this presentation. I go back to this when I get turned around or lost.
I loved it! Thanks!! Especially, thanks for spending hundreds of hours of effort and sharing it freely to improve the world's total beauty.
Love the visual examples! Thank you ❤
I have watched a half dozen videos explaining this and yours was the best for a super beginner like me. Thank you for doing this!! 👍
Say "God" and fedoras go flying. Anyhoo, the explanation in this video was great and I learned something from it. Fractals are awesome. They're in nature, too, like ferns or branches where the leaves repeat smaller and smaller. It's always fun to spot them.
It's been found that forests, themselves, are also fractal. As are structures in our bodies, and where the fractal begins to fail is the beginning of cancer!
@@zqxzqxzqx1 THE SOURCE POLICE, sir, can i check your Sources please?
@@adolfoalba1555 Sure. You have Google, right? Also NOVA.
Humans are fractals as well 🫁
The beauty of the maths, defining the most beautiful piece of art ever known, the "reality"
The mathematical explanation for what u see on DMT trips
oh I was finding the media materials like this. I'm so glad to use this video for my presentation. I apreciate you so much.
THANK YOU. You are the first person I have found that explains what dictates the hue of the colour
"Mandelbrot set: how it works and why it's amazing!"
Why thank you!
1:06 Wow this makes me want to learn complex math
3:19 Wow this makes me want to take LSD
ahaah this more like makes me want to take DMT
So that's what it is. I've seen this before and wondered, what's the big deal? Someone made some designs and now he's just zooming endlessly. Sure, must have taken some work, but okay, big deal, you made designs and it's trippy. Little did I know, this has to do with math. Like wtf. This is so weird and seems like it has something to do with the structure of reality itself somehow. Reminds me of strange things like the phibonacci sequence (that has to be spelled wrong).
Dan M btw its actually Fibonacci sequence
Lol phibonacci sequence. it's fibonacci actually, but phi does have smhng to do with the fibonacci sequence.
It has to do with math because it has a infinite perimeter but has finite area
The Mandlebrot set, like our reality, contains a mix of order and chaos, which is required for something like life to evolve.
Antonio Graciano would the area of it be irrational since you could never find an exact value?
I love the Mandelbrot set. Truly is inspirational.
" Sometimes there is no reason why " You figured it out, good for you!👏💪
THIS IS EPIC. THANK YOU!
no.........YOU'RE EPIC!! AND BEAUTIFUL
God is amazing. One day, when we are with Him, we will understand everything. God bless 🙏❤
Now I understand how psychedelics work.
Not really though
Thank you for explaining how the points are coloured. I've seen lots of videos of M. set but no one explained this.
Idk why I’m watching this since it’s summer break but it’s really cool
3:13 Mr. Stark, I dont feel so good
There’s no shot that was 5 years ago
@@ShadowDancer1000holy shit I was still in high school when I posted this. Time flies
3:32 "sometimes there is no reason why" *zooms in and music plays*
oh shit, mandelbrot is a vaporwave thing
that explains it aesthetic behavior
I always imagined it will eventually zoom into the infinite image of Nelson Mandela eating a bratwurst.
It's almost 1 am and I have work tomorrow morning but I'm just so mesmerized by this.
RUclips recommended a Mandelbrot video and I was going to comment what is it and why do ppl like it and this video was in the related section... PERFECT!
3:32 is what I’ve been trying to say to my friends who constantly ask me why the universe exists
It's like some Psychedelic drug psychedelic drug
Psychedelics reveal the truth of the universe.
quinxx12 Nah they just fuck u up pretty good
@@marionmoseby7490 how so? I know plenty of people including myself that can prove you wrong
And then there was Jimmy Two Times, who got that nickname because he said everything twice, like...
@@LyndonNLeeming22 imma go get the papers get the papers
Technically you created part of the image by choice of color scheme.
Good point!
Holobrine but he didn't choose where to put them, he just chose colors off the color spectrum
Actually he didnt choose the colors, the colors signify an integer value based on how far a number is from the value, each color representing a distance, "hot or cold" from the set
@@germanrud9904 but the image would be different if he asigned different Colours to different Numbers.
@@arthurg.machado6803 Only the colors, the structure, which is the important part here, wouldn't change by changing the colors.
"Sometimes, there is no reason why" is the best thing I have heard in a long time
The best basic explanation around -kudos to you, my man!
So, if you color every point that makes a loop in the mandelbrot equation black and every point that does not make a loop blue, where do all the other colours come from?
Alabastine I'm really glad this was asked and answered thanks guys.
ruclips.net/video/2JUAojvFpCo/видео.htmlm4s :)
Yea, at first there's only 4 colours, blue, cyan, pink and black, but by the end there's like a whole rainbow in there
is not just blue. he stated that the numbers are colour coded base on *how fast the number grows* , not if it forms a loop or not. for example, a number that increases by 2 is colour coded red, while a number that increases by 0.18287373 is coulored cyan. so is a spectrum of colours
Wow, Math really is cool !
"...then we get this shape."
*MANDELLYBROOT*
*brain machine broke*
ps: Whenever i see a video or something of a mandelbrot zooming in, i constantly feel paranoid. If anyone thinks im one weird b0i, im paranoid when i watch that because its like *falling through a void forever.*
Three things: α) AMAZING!
β) super AMAZING!!
γ) α+β!!!
Everlasting journey from nowhere to nowhere. Somewhere in "between" we spend some time in existence. In my humble opinion is better to reconsider the next time we feel sad frustrated or everything with negativity inside, because is such a waste of precious time. By the way, this is a very good presentation of the true structure of cosmos. As we say in Greece, thousands of years now, Αεί ο Θεός ο Μέγας γεωμετρεί (Πλάτων- Plato for π=3.14...^ ), because everything, eventually, "end up" and "start with" numbers.
Chris from Greece.
I didn't expect that mandelbrot set is a topic of mathematics 🤯🤯🤯
0:54 i find it funny that the expression of megacool is an explosion :)
Omg why can't they show this in schools it pisses me off !!!
Agreed.
And yet they also teach you a hypothisis that they claim is scientific law, even though it was debunked before the year 2000. ;)
Here is a link to a site that barely scratches the surface on what is wrong with the Big Bang.
In simple text.
No "Scientific jargon" to make it sound smart.
And it was done by Atheists, not "religious people"
science.howstuffworks.com/dictionary/astronomy-terms/big-bang-theory7.htm
@@sparkylongtail309 Nobody calls the Big Bang a "scientific law". It is not a law but a hypothesis. It has not been "debunked". The early history of the universe is not fully understood, but as far as I am aware, all models of the early history of the universe involve a Big Bang of one sort or another. Nobody can come up with a better model that doesn't involve a Big Bang of some sort.
I lost you at real and imaginary
Alanish yeah all you need to know is that a square root of a minus number is imaginary, and anything that isn't a square root of a minus number is real.
isnt a minus number imaginary itself?
+Art V. Minus number is not imaginary
@@artv.9989 Nope. And imaginary is the worst name ever chosen, because it makes it seem like imaginary Numbers are less valid than 'real' Numbers and they aren't.
All numbers are imaginary. Real numbers are just as abstract as “imaginary” numbers, they are just more intuitive
The clearest explanation in the world!
Fantastic!
If people get triggered over the mentioning of god, then we actually might be doing the opposite of becoming an advanced civilization
but how the fuck am I supposed to have my guilt-free rape dungeon if god exists huh??? how the fuck am I supposed to do that???? THIS RUINS EVERYTHING
*tips fedora*
SoItWouldBe? Lol in the future nobody is gonna believe in god
Karan Lal Lol people have been saying that for hundreds of years
Karan Lal Im an atheist but hol up a sec...just think about this. The big bang theory that states that everything came from nothing is just as ridiculus as saying that a higher power created the universe.
maybe people get offended by the mentioning of god because they know how ridiculous the idea of "god" is? lol
There is no way your mind does not blow, if you understand this...
I understand it.
Math is a logical creation, and consistent with itself.
It is so simple a small child can understand, but so complex that it baffles the greatest minds of history.
That's why I always say, if there is a God, he/she is great mathematician. Julia and Mandelbot fractals are one of my favorites.
KarmicYogi not only that but a great artist. Think of the sculptures of life he structured, the colors he painted (both seen and unseen) and the symphonies he composed (both heard and unheard). Amazing...
which make think that we are not as important as we think, human have always like to be the center of the universe.
KarmicYogi there is no fucking god 😂 I always laugh at comments like this
Anna Dello i'm sorry did you read the part where it said "if there is a god" this does not say their is or isn't just *if* there is
Anna, prove it.
This is the best video for this topic. I didn’t understand and I frantically took to Google to find the answers but I was dumbstruck. This video cleared it up for me.
this may be one of the best mandlebrot set videos on the interwebs. MEGA COOL
Almond bread
My brain hurts
Same
0:21
The lack of parenthesis around the -n upset me deeply.
I’m
I am not sure what i am looking at, but doubtless its the most beautiful thing i have seen in my life.
Stop it you’re hypnotizing me...THIS THING GOES ON FOREVER AAH
Who needs lsd when you have maths.
beautiful
Blue J trust me, math on lsd is beautiful, but it is not necessary.
The comments on these sorts of videos seem to be divided between people who appreciate the knowledge and people who take drugs. I suspect that the intersection of that Venn diagram is pretty close to empty.
awesome :) Sad that people fear what they don't understand and will then blame you for it. I like your reference to God. It's an interesting analogy for an incomprehensible concept.
3:08 Most people argue about this being an "argument from ignorance" for God, but I'm more worried about you saying "no one designed this" and immediately followed with "God created this." What's up with that?
Alficiro I don’t think he literally meant God. I think he was making an analogy to God because of how complex the whole thing is
Why are you triggered?
Best quick explainer I've seen so far. But then I'm mathematically reclined.
Underrated video. Very good explanation
Recently, i have been seeing in my suggestions about some dude zooming into some kinda image, and I was like"What the hell?" Now i get it....Its much more complicated....😅🤔
Started with maths and ended with god.....
Guru Boss shhhh 🤫
But something did create it so there is a reason why.
That's the tie dye colorful hallucinations you see on hallucinogens. The fingerprint of the source. Beautiful I love it.
I love it! It is one of my favorite Mathematical formulas. Why didn't they teach me this in Grade 4? They should teach this in Grade 4 to install a sense of wonder and love for Maths. It's so easy yet so complex in beauty.
my mind exploded because im a 7th grader in algebra and i do not know one single crap of what youre talkimg about
Just keep doing problems. Try doing a single algebra problem per day. Understand functions and their inverses. What is the inverse function of x^2 ?
Same here
Proof we live in a simulation haha
Julia XD
What
No. It proofs that there is a creator
YYZY how is this proof for a creator?
YYZY if we live in a simulation then someone created it.
Math gone too far
it works, amazing
I don't understand most of what he is saying ,but this is truly beautiful
Wut
Chill out, God haters. There is nothing wrong with finding and explaining the wonder in Creation.
Your treatment of science as a religion is dangerous.
"God haters" I don't hate god, in fact I believe there _might_ be a possibility of a god, but there's no proof. Like a simulation. I just don't accept god being here because this just has to do with math.
What is wrong is desperately trying to find something where to find "God" cause you just cant find him anywhere. This is just a color coded graph...
How can you hate something that doesn't exist? And humans created math
This neither finds nor explains creation.
We created the math, which is just a tool to formally define patterns and logic in nature. Math is a toolkit that allows us to see a lot more about the nature of reality than the naked eye does, and some things seem to work out so seamlessly it's not strange to believe in a concept like god.
I understand the vision @CMC A holds because I used to used to be a full blown atheist, but there are in fact countless of metaphysical examples that can not be explained through science alone. Some things simply can not be expressed and have to be experienced. Try proving formally that beauty exists. You can't. There are limits to rational thinking, hence why our ancestors used countless of stories in the bible and other writings to make sense out of those things that can not be explained otherwise.
All of the sudden: 'In this image, I see god.' Uhm... Okay?
Please remind me to watch this again after a few days, we have our calculus exam tomorrow. Thankyou!😁
I remembered what this video said, recited the main points of this during class and put a smile on my teachers frown lined face
mentioning god in a scientific context just shows ignorance
@Matt Eru boom!!.....drop it like it's hot
All science is simply an acknowledgement of what God has created and sustains. And science is constantly changing, whereas God never does.
God and His Word are infallible, whereas man & his observations are not.
Pfft "atheists"
lol a creationist
Pfft "creationists"
Pfft "edgelords who think God doesn't exist"
Pfft "people who generally don't care"
Pfft
Friend. I am so greatful for your video inwhich you explained it very good. You covered many holes i had researching this mandelbrot subject. You got me closet to understanding. I only dont understand why : you pick random numbers and if the formula determines that the result is exponential results - then its not in the mandelbrot setup. You rlly explained it veryvery good, thanks. but plz explain it like i am 3 years old. You left some holes in the logic you were following. I rlly rlly rlly want to understand this. You rlly helped me!!
This makes just so much sense! Thank you!!!
Just awesome! Nice video. Thanks.
I was looking for this. So easily explained how that shape is generated. Thank you so much.
Thanks for making this easier to understand! Really enjoyed this video. I see so many designs in creation in this set
The best explanation o I've seen.
This just gave me chills