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
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
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.
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.
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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.
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)
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 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
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?
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!"
