Julia Sets, and how they relate to The Mandelbrot Set
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- เผยแพร่เมื่อ 10 ก.ค. 2024
- A little video introducing Julia Sets as a follow-up to the Mandelbrot Explained video. In this video we have a little look at the Julia Sets and where we find them embedded into the Mandelbrot Set. This was going to be a longer video, but I've broken it into two parts, in the next video we look into how to "build a Julia Set" using complex transformations. Please subscribe!
Some terminology: In this video I refer to the set being "dust" because it is "infinitly disconnected", in more mathematical contexts you may see this referred to as "Cantor set" or "Fatou Dust".
If you loved this video then why not buy me a coffee: ko-fi.com/mathstown
In this video:
00:00 Introduction
00:33 Julia Sets
02:54 Types of Julia Sets
03:57 Map of the Julia Sets
05:18 Mandelbrot Set vs Julia Sets
06:10 Embedded Julia Sets in the Mandelbrot Set
07:18 The Mandelbrot Set Remembers
11:55 A Julia Set Zoom
In this series:
1 - • The Mandelbrot Set Exp... The Mandelbrot Set Explained
2 - • Julia Sets, and how th... Julia Sets, and how they relate to The Mandelbrot Set
3 - • How to Build a Julia Set How to Build a Julia Set
4 - • Number Sequences in th... Number Sequences in the Mandelbrot Set
Extra Visuals (No commentary):
• [Extra Visual] All orb... - All orbits of the Mandelbrot
• [Extra Visual] All Per... - Period 1 orbits of the Mandelbrot
• [Extra Visual] All Per... - Period 2 orbits of the Mandelbrot
• [Extra Visual] Buildin... - Building a Mandelbrot step-by-step
• [Extra Visual] Period ... - Period 2 orbits of a Julia Set
• [Extra Visual] Period ... - Period 3 orbits of a Julia Set
• [Extra Visual] Period ... - Period 4 orbits of a Julia Set
• [Extra Visual] Period ... - Period 5 orbits of a Julia Set
• [Extra Visual] Period ... - Period 6 orbits of a Julia Set
Includes content from:
Music: audionautix.com
11 Dimensions Video: • 11 Dimensions in 8k - ...
Accidental Masterpiece: • Accidental Masterpiece...
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
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.
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
This is so poetic. Julia sets are either whole or dust
Yeah I understand
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
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 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.
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
So Mandelbrot's is kind of Juslias' atlas. Probably most beautiful entity out there
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.
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
This should be on the next Golden Disc we send out
An exceptionally constructed tour
yay thnx for the high quality upload
Absolutely awesome
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 am inspired by this. thanks for what you do.
what an incredible render!
Informative and interesting. Thank you. :)
I feel like I'm on acid
Mathematics really are a beautiful, mysterious creation in their own way.
Very interesting - thanks for positing.
Amazing to behold.
Fascinating and great content, I think your page will blow up among maths fans
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!
What software did you use to generate and explore the sets on screen?
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.
Beautiful
Awesome content
mind blowing
When the map of julia sets in the complex plane was revealed to be the mandelbrot set, i audibly screamed.
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.
Being a Julia myself, i somehow know how it feels, man.
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
i am watching this and happy but its even lower quality.
best experience.
4:54 i loved how the mandlebrot set just lit up like a cristmas tree
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?
Great video
what program is being used to give us these visuals? i would love to play around with it later myself
3:10 pause perfect
4:30 to 4:55 is the biggest plot twist in math I’ve ever seen
That's awesome!! the fractal is gorgeous and I wonder what software you use to generate a fractal?
It's beautiful, and mildly terrifying.
Yes the cool fractals!
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
i wish the julia set got more attention, it seems like its almost the "mother" of the Mandelbrot set
Love the fractal content!
Z = Z² + C
When the detail is shown of the grid of julias that is zooming all of the julias to do that? If so, how far?
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
This video is informative, why very small people watch this video?
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.
What coloring function are you using?
Mandelbrot is the DNA of Julia sets
What is the julia set value for the one in the thumbnail?
how did you make these animations?
are there any other sets or are they all based of from the mandlebrot?
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.
4:00 can you tell the formula for the julia set images please
3:11
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.
Bravo! Bravo!
U can find Julia sets IN THE MANDELBROT SET
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.
Order in the chaos or chaos in the order?
😎😎😎😎
If you find a Julia set containing 10 or fewer pieces, let me know.
God Bless my sun ❤️🌞💞❤️❤️
Here before Deseptor and Borchie the Oof God
I wonder if the quaternions and octonions have a weird nature around zero as well
0:75
micro nano universe 👍♥️
Agradecería mucho q los subtitulos los pongan en español, si les interesa, gracias
🌏
11:03 me having the illusion of smashing into the walls of the Juliet set
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"
Map of the 3d multiverse
epic
c=0.3 escape
c=0.2 bounded
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.
I feel that my brain has been rewired and I don’t even know why
"and why they form the shapes they D-" - The Mathemagican's Guild
You can find an embedded Julia set in an embedded Julia set
U can sort of already see the Mandelbrot set at the first map of Julia’s it’s hard to see
Yeah, thanks mate. Now I can't walk to the fridge. Maybe if I watch it backwards my brain will reset,
Fractals are cool!!! 😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎😎
ジュリア集合とマンデルブロ、形まで連携しているとは思いもよりませんでした
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!"
Embedded Julia sets are in some zooms
So start z = z^2 + c
Second
D(f(f
(Tried to spam at 197)
Being able to think on a quantum level allows me to use this data to know how my whole life will pan out, if I dont make an error and die
Mandelbrot is kind of Julia Mashup.
Magic Mushrooming Nature
O_O I just said you can create math
Mini mandelbrots
Find a minibrot in embedded Julia set
Tracey or Mandelbrot set