My mind was blown when you showed that the infinite lower branches actually remembered their main one. You have created a truly masterpiece with this series of vides about fractals, really I say it from the deepest of my heart, you made something so complicated understandable to everyone, this whole series should be a feature lenght documentary. Again, BRAVO!
@@eduardomeza7279 reality is a fractal of oction hypercomplex dimension. That's why we have complex numbers in the quantum mechanism equations. The multiverse is hypercomplex
Fractals, holography, cellular automata, and dissipative structures, are most of the ingredients you need to make an evolving universe replete with consciousness. If you take a high dose of psychedelics, your consciousness hologram will fractally splinter, and you will see by being exactly what you're intuitively intimating here.
This was really mindblowing and still i dont completely understand what im watching. Ive fallen in love into fractals and been watching and "studying" them for like 10 years. Everytime i dive deep into these i always find myself confused about its beautiness. I want to learn to understand it more deeply.
@@xxzoomfractalchannelxx8676 yes i understand that. But the outcome is what is mindblowing yet so simple calculation can have such a complex outcome. Julia sets for sure are more simplier than some fractals tho.
Even though I am a person that is really bad in math, and is unable to understand the equation, this video has completely mindblown me in a positive way, I just really love fractals
This, holography, cellular automata, dissipative structures and autopoiesis, are most of the ingredients you need to make an evolving universe replete with consciousness. Fantastic video. Subscribed.
Honestly the relationship between the 2 is SO interesting I never knew this!! And the part where the branches can remember where they were at, that is SO COOL as well
At 11:16 when you say, "And there is our original embedded Julia with about six spirals". This moment, as well as the earlier when the Mandelbrot set emerges from the infinitely small sets, were revelatory. Bravo, my good man! How can any even moderately curious mind not be inspired by this demonstration?
I'm not sure if I missed it (or it comes later), but the shape of a mini Julia in the M set looks just like the Julia set for the c of that region. So not only is the M set an index to Julia sets, it also previews for you what they will look like. What could be better than reading the title of a book and immediately knowing its contents?!?!
Thanks for such a nice video explanation! Earlier tonight I was like..."Why did I spend so many hours today studying how to make fractal shaders???" and then that zoom started...and I was like: "OH THAT WAS ACTUALLY WORTH LEARNING!!!" Can confirm if this understanding of difference between Mandelbrot and Julia shader calculations is correct?: Main difference is seemingly that a Mandelbrot set has a C val that changes every pixel as it basically seems to do a “for loop” style scan across each row of texture coordinates row by row in the entire frame. So at each point it is calculating the pixel color for, it inputs that texture coordinate under that pixel as C. In a julia set Z is initially set to the texture coordinate it’s rendering the pixel color for, but C is a constant coordinate val that is shared by every pixel (texture coordinate under the pixel) calculation and that val is from a specified n+i plane coordinate selected. (so in an interactive shader, the coordinate under the touch is C and then Z is every pixel coordinate in a similar “for loop” style row by row scan as the Mandelbrot). That is seemingly how that functions. Would like to understand better about how "zooming" is done mathematically and generated by a fractal shader.
i like this julia set remembering that happens on the fractal, it can make some really chaotic zones, like in the bulb near the 0.25+0i point, the patterns get further and further away essentially making little elephants
This is the best argument for mathematical Platonism. To think such beauty is not discovered is sheer arrogance about the creativity of the human brain, no less ridiculous than the error of solipsism.
There are currently 48 comments (49 with this one), 21 059 views and around 2.18*(10^3) subscribers. This channel's growth is going to simulate the Big Bang soon!
4:00 Hi, i have a little question, i understand that in every pixel from complex plane c value you graphed the corresponding julia set, but why when you decreased the zoom did they turned into black color?
i love all the different color schemes you use when displaying your mandelbrot sets... i even found a non-binary flag in one of them! (it was roughly at the timestamp 5:08, it's the part between the main cardioid and the other circle-ish shaped doohickey. you know, the one with the double-orbit)
So would it be correct to say that a Julia set is a way of understanding one of the infinite possible paths you can take to zoom outwards from the Mandelbrot set to the infinitely large Mandelbrot set that it is part of? (I am thinking of a fractal here in a slightly different way - not as a shape that contains smaller versions of itself but as a shape which is part of an infinitely large version of itself.)
I don't really know what I'm saying but I'm pretty sure that fractals or at least the Mandelbrot set aren't infinitely big but actually fit into a finite space. I think this because the approximate area to the Mandelbrot set has been figured out already and it's close to 1.5 which definitely isn't infinity. The infinite part of the Mandelbrot set would be the perimeter since you could keep zooming in infinitely but if you zoomed out you would actually reach a point where you could see the whole Mandelbrot set in its entirety (which is where most mandelbrot fractal videos start).
@@kahiauquartero6258 Yeah, I understand that, but when I was thinking of the infinitely large concept, I was thinking in a slightly different way. The way you describe it takes the unit of measurement as being the normal scale of numbers on the complex plane - the scale of the whole Mandelbrot set. But the way I am thinking of it is like taking the unit of measurement as being the infinitely small mini-brots that you find inside, so if that infinitely small thing was equal to one unit, things like the whole set that are measured by finite units normally, would be seen as infinitely big.
Thanks for the video, was really helpful but I do have one question. I'm currently working on fractals for a school assessment, and it would be really useful if I could use the software you were using here. I was wondering, what is this software? There's a fair chance I won't be able to run it (none of the software I could find runs on macOS Monterey), but it looks really helpful. If anyone can point me to other strong software as well that would be nice as well
Throughout watching, I kept counting the spirals, and everytime you'd stop, I would go: "Oh, there's the Mandelbrot now! No..? Ok, let's keep going, I guess. . . . Is there one here? No? Keep going... . . . There should be one here now, right? Aaand there isn't." _O N E E T E R N I T Y L A T E R_ "Ok, 32-way-symmetry... Oh, finally, a Mandelbrot!"
Would like to better know what is happening at that last step between that grid of julia sets and fully rendered Mandelbrot. That is a zoom on every one of those julia sets or...?
So then does that mean there exists a 4 dimensional (or 2 complex dimensional) mandelbrot-julia set? Where one complex number range is z and the other is c. What properties would that have?
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The fact that iterations of a simple equation can generate patterns as complex as this is mind-blowing
Not really though
@@silvermediastudio it reallly is though
@@silvermediastudio are you disinterested in everything?
@@yourtypicalcupoftea No, I'm just not mind blown that an equation can produce a pattern. That's exactly how formulae and variable plotting works.
@@silvermediastudio oh
4:30 - 4:40 COMPLETE MINDBLOWN
This channel really deserves to blow up
Yeah, I was astonished, as I was thinking "how can this be true?" and "of course, it's so natural" at the same time!
@@arancedisicilia75 because they're related? it should be expected not surprising. your intuition is pretty bad.
10:25-10:50 also blew my -ABSOLUTE- mind
My mind was blown when you showed that the infinite lower branches actually remembered their main one. You have created a truly masterpiece with this series of vides about fractals, really I say it from the deepest of my heart, you made something so complicated understandable to everyone, this whole series should be a feature lenght documentary. Again, BRAVO!
Thanks for the kind comments. I’m glad I could share some of what I find fascinating.
❤AGREED
This is so poetic. Julia sets are either whole or dust
Yeah I understand
Every time I look at these it feels like I’m looking at some hidden important information about existence.
The whole universe is a fractal. Breaking life down into abstractions helps understand the recursive and fractal nature of its different aspects.
Could this be how the whole universe looks like?
@@eduardomeza7279 reality is a fractal of oction hypercomplex dimension. That's why we have complex numbers in the quantum mechanism equations. The multiverse is hypercomplex
It’s a glimpse at the mind of God.
Fractals, holography, cellular automata, and dissipative structures, are most of the ingredients you need to make an evolving universe replete with consciousness.
If you take a high dose of psychedelics, your consciousness hologram will fractally splinter, and you will see by being exactly what you're intuitively intimating here.
This was really mindblowing and still i dont completely understand what im watching. Ive fallen in love into fractals and been watching and "studying" them for like 10 years. Everytime i dive deep into these i always find myself confused about its beautiness. I want to learn to understand it more deeply.
A simple calculation can make a Julia set
@@xxzoomfractalchannelxx8676 yes i understand that. But the outcome is what is mindblowing yet so simple calculation can have such a complex outcome. Julia sets for sure are more simplier than some fractals tho.
Even though I am a person that is really bad in math, and is unable to understand the equation, this video has completely mindblown me in a positive way, I just really love fractals
So Mandelbrot's is kind of Juslias' atlas. Probably most beautiful entity out there
This, holography, cellular automata, dissipative structures and autopoiesis, are most of the ingredients you need to make an evolving universe replete with consciousness.
Fantastic video. Subscribed.
I wouldn’t quite say so
Honestly the relationship between the 2 is SO interesting I never knew this!! And the part where the branches can remember where they were at, that is SO COOL as well
It is incredible that these insanely complex and varied images are a product of logic itself
And then he...looked at a romanesco...and noticed how organic things are "designed".
At 11:16 when you say, "And there is our original embedded Julia with about six spirals".
This moment, as well as the earlier when the Mandelbrot set emerges from the infinitely small sets, were revelatory. Bravo, my good man! How can any even moderately curious mind not be inspired by this demonstration?
Your videos are the best explanations of Mandelbrot/Julia fractals I've seen.
Mind blown. Great video, this needs more views!
Thank-you.
An exceptionally constructed tour
I'm not sure if I missed it (or it comes later), but the shape of a mini Julia in the M set looks just like the Julia set for the c of that region. So not only is the M set an index to Julia sets, it also previews for you what they will look like. What could be better than reading the title of a book and immediately knowing its contents?!?!
I have really appreciated this series. Well done!
Fascinating and great content, I think your page will blow up among maths fans
This should be on the next Golden Disc we send out
Thanks for such a nice video explanation! Earlier tonight I was like..."Why did I spend so many hours today studying how to make fractal shaders???" and then that zoom started...and I was like: "OH THAT WAS ACTUALLY WORTH LEARNING!!!" Can confirm if this understanding of difference between Mandelbrot and Julia shader calculations is correct?:
Main difference is seemingly that a Mandelbrot set has a C val that changes every pixel as it basically seems to do a “for loop” style scan across each row of texture coordinates row by row in the entire frame.
So at each point it is calculating the pixel color for, it inputs that texture coordinate under that pixel as C.
In a julia set Z is initially set to the texture coordinate it’s rendering the pixel color for, but C is a constant coordinate val that is shared by every pixel (texture coordinate under the pixel) calculation and that val is from a specified n+i plane coordinate selected. (so in an interactive shader, the coordinate under the touch is C and then Z is every pixel coordinate in a similar “for loop” style row by row scan as the Mandelbrot).
That is seemingly how that functions. Would like to understand better about how "zooming" is done mathematically and generated by a fractal shader.
yay thnx for the high quality upload
What software did you use to generate and explore the sets on screen?
I feel like I'm on acid
Mathematics really are a beautiful, mysterious creation in their own way.
i like this julia set remembering that happens on the fractal, it can make some really chaotic zones, like in the bulb near the 0.25+0i point, the patterns get further and further away essentially making little elephants
4:54 i loved how the mandlebrot set just lit up like a cristmas tree
Feels like glancing into an overwhelming and beautiful infinity that can leave a weak mind a little insane.
By the way, thank you for the nice music at the end. It helps.
Being a Julia myself, i somehow know how it feels, man.
Love the fractal content!
Z = Z² + C
i am inspired by this. thanks for what you do.
This is the best argument for mathematical Platonism.
To think such beauty is not discovered is sheer arrogance about the creativity of the human brain, no less ridiculous than the error of solipsism.
It pains me a little, but I have to agree
There are currently 48 comments (49 with this one), 21 059 views and around 2.18*(10^3) subscribers.
This channel's growth is going to simulate the Big Bang soon!
It's beautiful, and mildly terrifying.
what an incredible render!
4:30 to 4:55 is the biggest plot twist in math I’ve ever seen
Very interesting - thanks for positing.
When the map of julia sets in the complex plane was revealed to be the mandelbrot set, i audibly screamed.
Absolutely awesome
i am watching this and happy but its even lower quality.
best experience.
Awesome content
Amazing to behold.
3:10 pause perfect
That's awesome!! the fractal is gorgeous and I wonder what software you use to generate a fractal?
i wish the julia set got more attention, it seems like its almost the "mother" of the Mandelbrot set
This video is informative, why very small people watch this video?
Informative and interesting. Thank you. :)
what program is being used to give us these visuals? i would love to play around with it later myself
When the detail is shown of the grid of julias that is zooming all of the julias to do that? If so, how far?
4:00 Hi, i have a little question, i understand that in every pixel from complex plane c value you graphed the corresponding julia set, but why when you decreased the zoom did they turned into black color?
i love all the different color schemes you use when displaying your mandelbrot sets... i even found a non-binary flag in one of them!
(it was roughly at the timestamp 5:08, it's the part between the main cardioid and the other circle-ish shaped doohickey. you know, the one with the double-orbit)
(for anyone who doesn't know, it starts with yellow, then white, purple, black)
There are SWASTIKAS on the TEMPLES in japan and I made an app that can make a fractal of beautiful SWASTIKAS.
Mandelbrot is the DNA of Julia sets
Yes the cool fractals!
Order in the chaos or chaos in the order?
So would it be correct to say that a Julia set is a way of understanding one of the infinite possible paths you can take to zoom outwards from the Mandelbrot set to the infinitely large Mandelbrot set that it is part of? (I am thinking of a fractal here in a slightly different way - not as a shape that contains smaller versions of itself but as a shape which is part of an infinitely large version of itself.)
I don't really know what I'm saying but I'm pretty sure that fractals or at least the Mandelbrot set aren't infinitely big but actually fit into a finite space. I think this because the approximate area to the Mandelbrot set has been figured out already and it's close to 1.5 which definitely isn't infinity. The infinite part of the Mandelbrot set would be the perimeter since you could keep zooming in infinitely but if you zoomed out you would actually reach a point where you could see the whole Mandelbrot set in its entirety (which is where most mandelbrot fractal videos start).
@@kahiauquartero6258 Yeah, I understand that, but when I was thinking of the infinitely large concept, I was thinking in a slightly different way. The way you describe it takes the unit of measurement as being the normal scale of numbers on the complex plane - the scale of the whole Mandelbrot set. But the way I am thinking of it is like taking the unit of measurement as being the infinitely small mini-brots that you find inside, so if that infinitely small thing was equal to one unit, things like the whole set that are measured by finite units normally, would be seen as infinitely big.
There is a never ending amount of extreme information you can get from fractals
and its not actually that hard to figure out the basics or generate images
real study would probably be graduate level otherwise you'll just get very beautiful pictures :)
In 3D the graph repeats as well no matter how many times you zoom in from any direction or angle
which if true is enough to know that that are certain points of space that contain infinite space inside of them in which you can zoom into
and then at the bottom of that point is another point inside of that
Here before Deseptor and Borchie the Oof God
Thanks for the video, was really helpful but I do have one question. I'm currently working on fractals for a school assessment, and it would be really useful if I could use the software you were using here. I was wondering, what is this software? There's a fair chance I won't be able to run it (none of the software I could find runs on macOS Monterey), but it looks really helpful. If anyone can point me to other strong software as well that would be nice as well
Throughout watching, I kept counting the spirals, and everytime you'd stop, I would go: "Oh, there's the Mandelbrot now! No..? Ok, let's keep going, I guess. . . . Is there one here? No? Keep going... . . . There should be one here now, right? Aaand there isn't."
_O N E E T E R N I T Y L A T E R_
"Ok, 32-way-symmetry... Oh, finally, a Mandelbrot!"
mind blowing
Would like to better know what is happening at that last step between that grid of julia sets and fully rendered Mandelbrot. That is a zoom on every one of those julia sets or...?
This video makes me remember the bifurcation diagram (n×r(1-n), because as r gets bigger, the results become More chaotic
The bifurcation diagram is also the Mandelbrot set, in that the period of each bifurcation maps to the regions of the set with that period.
Great video
So then does that mean there exists a 4 dimensional (or 2 complex dimensional) mandelbrot-julia set? Where one complex number range is z and the other is c. What properties would that have?
Yes it does! I haven’t explored it too much yet though.
What is the julia set value for the one in the thumbnail?
c=0.3 escape
c=0.2 bounded
are there any other sets or are they all based of from the mandlebrot?
I wonder if the quaternions and octonions have a weird nature around zero as well
Beautiful
U can sort of already see the Mandelbrot set at the first map of Julia’s it’s hard to see
micro nano universe 👍♥️
I don't know how to link the time stamp, but 8:05 looks like a growing point on a plant.
"Let's have a closer look"
3:11
4:00 can you tell the formula for the julia set images please
U can find Julia sets IN THE MANDELBROT SET
What coloring function are you using?
Does this make the Mandelbrot Set a Julia Set? Is it the Emperor of Julia-Setkind?
You can find an embedded Julia set in an embedded Julia set
how did you make these animations?
Bravo! Bravo!
😎😎😎😎
Embedded Julia sets are in some zooms
A filled Julia set is also known as a "stable Fatou set".
Or "connected juila set"
@@B_boy5239 No, a "connected Julia set" is the boundary of a stable Fatou domain.
If you find a Julia set containing 10 or fewer pieces, let me know.
11:03 me having the illusion of smashing into the walls of the Juliet set
Map of the 3d multiverse
Yeah, thanks mate. Now I can't walk to the fridge. Maybe if I watch it backwards my brain will reset,
God Bless my sun ❤️🌞💞❤️❤️
There isnt supposed to be much black in the image
0:75
"and why they form the shapes they D-" - The Mathemagican's Guild
Agradecería mucho q los subtitulos los pongan en español, si les interesa, gracias
O_O I just said you can create math
So start z = z^2 + c
Second
D(f(f
(Tried to spam at 197)
Fractals are cool!!! 😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎
Find a minibrot in embedded Julia set
Mandelbrot is kind of Julia Mashup.
I feel that my brain has been rewired and I don’t even know why
Tracey or Mandelbrot set
epic
It's not really supposed to "move" especially not like that