Deepish - Mandelbrot Fractal Zoom (e2656) (4k 60fps)
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- Опубликовано: 28 авг 2024
- A deep zoom all the way to a magnification of 4e2656 (that is 4 with 2656 zeros after it). Imagine if your camera could do that! A clasic colouring and some trap sounds from "Damma Beatz" for this zoom. It's a long one so if you don't enjoy my music selection, play something of your own.
As usual, I have disabled mid-roll ads, so you can enjoy this 3 hour zoom uninterupted.
All these infinite shapes and patterns are created simply by calculating the equation "z=z²+c" over and over again. How such a simple equation creates such intricate shapes is one of the many wonders of the mathematical world.
Thank-you to my supporters on Patreon.
This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. / mathstown
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#Mandelbrot #fractal #mathstown #fractals
Zoom: 4.7e2565
Iterations: 591202796
The location info is too big for the description, you can find it here: www.maths.town...
![Infinite Relaxation [Part 1] - A Mandelbrot Fractal Zoom (3e3284)](http://i.ytimg.com/vi/6ouG6L-2L3Q/mqdefault.jpg)
![Infinite Relaxation [Part 1] - A Mandelbrot Fractal Zoom (3e3284)](/img/tr.png)
Let give a moment to respect to the cameraman
😂😂😂
lol
Didn't care about shattering his bones at the bottom of the fall [IT'S FOR THE CONTENT].
@@XE1624 Don’t worry, the money will cure him.
The Mandelbrot set is the DNA of the universe.
This is beautiful and relaxing. Thanks!
Thank-you!!!
@@MathsTown
Question:
With Fractals you can 'Zoom in' infinitely, BUT....
... "What happens if you Zoom out"? (from the starting Mandelbrot set)
Our computers in the early '90's just gave an us an ERROR OUT OF RANGE when we tried it at university,
and we never had as much detail in our renders when we 1, displayed the full set & 2, when Magnified. The image was a bit janky at first but it slowly built to a higher resolution on the still frames.
This was to be expected as the Main frame 'only' had 64meg storage capacity with an AMD processor from 1989.
They kept updating the Math processor module but had to bite the bullet & they got a new main frame in 1993 with 512meg and dual core processors (not sure of clock speed). Cost over £600,000!
It didn't get set up till August after we had graduated.
@@nigelnightmare4160 Awesome question! But not so awesome of an answer... If you try to zoom out of the mandelbrot set, all you will see is one solid color engulfing it, and then you will only see that color on the screen, with that tiny spec of the mandelbrot set in the center, then you will only see the solid color. This disappointing result is because every point within the mandelbrot set can not be more than 2 units away from the origin of the complex plane. One unit takes up most of the Mandelbrot set itself.
However, there could be other fractals out there where you can zoom out and see as many wonderful things as you would zooming out, but I do not know any on the top of my head. I do know that fractals related to the Mandelbrot set, such as the Julia Sets, Multibrot Sets, Buddhabrot sets, The Tricorn, and The Burning Ship, also do the same thing; where the entire set is engulfed by one solid color.
Such beautiful structures along the way. Excellent video!
I can't wait to watch this on my new 75" TV.
God I love this one❤ ty
Amazing as always.
On acid is crazy. Thank you
bro. i didnt know i was supposed to watch it cross eyed
amazing
You wanna see something really trippy? Stare at the center for two minutes then look at your hand.
This video was a very nice surprise.
Good fractal for Mandelbrowser
Z² (Z + 2) + C
Idk what it's actually called but I call it the Exploded Needle.
It looks like a regular Mandelbrot but the needle didn't want to be a needle anymore
Haha I use mandelbrowser too and I also made some crazy fractals with it
This is so amazing!
Mesmerising, thank you!
At it again with the classic M set and its electronic seahorses-issue shapes. Nice one :-)
Always awesome. Now you need to animated the colors. 🤘😎🤘
If you wanna see something real trippy stare at the exact center for two minutes then look at your hand.
I get baked during and after watching your videos.
You almost reached your 100k suscribers :)
amazing work
Can you make one that goes through a huge part of the needle?
Stunning
seems like compression removed details
Beautiful but had to slow it down to really enjoy it. Would be cool to see thease in reverse like your blasting off looking back.
How am I just finding this? Numbers don't lie!!
This computer generated Mandelbrot sequence plays out what is happening within the 3rd, 4th and 5th dimensions. Example:
As you move downward in the rabbit hole, how can there be light? Where is its source?
How long did it take to render?
Maths town>Mandelbrot set
Mandelbrot set>other parts of math
Still master of color, light and shadow
How many teraflops do I need to generate this in real time, for example for a screen saver?
STOP MISSING THE CENTER!!!
If he went directly to the center it would be black.
me when falling into the everlasting void
Nearly 100k subs
are some of this zooms done in a way that they look like constantly "jumping" or i have a problem with the software of my phone? with hardest trip and with golden trap the zoom was flowed but with hardest trip 2 and with this one it looks "jumpy"
Nearly 100k subs silver play special
Ultracool!!!…🤙😎🤘
Yea
That good math bro
How many values of z are on the screen at one time? Question 2, does the program used to generate the picture calculate the whole Mandelbrot set or just the part showing on the screen? Please respond. Thanks. Now i will start the video over. Amazing.
1) There are no z values on the screen. But each pixel of each frame represents a different complex number c. To render each pixel, the "z=z²+c" was computed up to 591202796 times - the color of the pixel is derived from the actual number of iterations used for that point. The vast majority of what is seen in the video is not actually in the Mandelbrot set itself, but its surrounding. Only the completely black pixels took the maximum number iteratations to be computed - and only those are considered to be part of the set. (The very dark parts of the color gradients are not actually black).
So you could say, that in theory, somewhere between 3 × 60 × 60 × 60 × 3840 × 2160 × 1 and 3 × 60 × 60 × 60 × 3840 × 2160 × 591202796 z values were used to computate this video (it is probably closer to the lower estimate, becase the software used to generate it does some clever optimizations).
2) It is not possible to calculate the whole set, everything is just an approximation to some degree. Some of those black point near the borders might still not actually be part of the set, but it would take infinite number of iterations to find out for sure. The points can be calculated independently of each other, so only the pixels that are visible were calculated - unless there was some cropping done.
@@drahoslove thank you so much. Great info. Im trying to learn on my own but can i ask is the picture on the screen 2 dimensional even though its curvy beautiful shapes look 3 dimensional?
@@frankconley7630 The Mandelbrot set is 2 dimensional (there are two axes in the complex plane: real and imaginary dimension) - so the two cooridanates of the point (pixel) on the plane (screen) is the complex number c. The whole sets lays within the circle with radius of 2 - so all the c numbers are pretty small.
Each point either belongs to the set, in which case it is usually colored black - or it does not belong in to the set, in which case it should not be colored black. There is a huge variety of possible interpretation of the "not black". It is just a matter of an artistic liberty of the author, it is unrelated to the definition of the Mandelbrot set. The shading in this video, which makes it looks 3D-ish, is just to make it more visually interesting.
If you want to imagine the numbers behind it:
- the input for the computation of each frame is the matrix of complex numbers - the coordinates (the c values - one for each point).
- the output is the matrix of integers - the number of iterations for each point (how many times the function "z=z²+c" was itarated over for this c value until the z value left the boundary of the 2-circle, or until the max number of iterations was reached. The z value is then thrown away; only the number of iteratons is the interesting result.) At the beginning, the z is always 0+0i.
Each number of the output matrix is then visualized as pixel colored folowingly:
If the number is equal to the predefined maximal number of iteration (591202796 in this case, but should be infinity for the exact result) then it would be black. If it is less than that, then it is usually colored using a color on some cyclic color gradient (the position on the gradient is somehow determined from the iteration value, but the math behind that si not trivial, involving logarithm and possibly some density statistics - it is outside of the scope of the Mandelbrot set definition). In this case, it looks like the palette of the gradient also contains the black color, which makes the result more appealing because of the high contrast, but also more confusing, because you don't know what is actually the set and what is just artistic expression (see 0:00:17 - the obvious black minibrot vs the outer black layer easing from and out of the white.)
Thank you my sun ❤️❤️God Bless my sun ❤️ 🌈☀️
If you mean son I'm with you.
هل يفيد لكسل العين للبالغين
Just found your channel. My brother in-law joked he was going to do DMT to your videos... I'll try my best to not let this happen. I love your videos and I don't have to be high to watch them cuz there so good 👾☺️
Don't, you should try it too :)
Is there anywhere i can download a full bitrate version?
What do you use to generate these?
Maths Town, What fractal image generator do you use? Kalles Fraktaler?
I think it's Mandelbrowser.
@@Gardengap How? It can go further than e300, can upload more iterations, and more stuff like that.
@@ilovefractals1729 idk
Why does it always shapes like a circle at the end
I don't know. It's something to do with how it works.
ez way to get high
зачем вы так дорисовываете. ведь заметно, что это ненатуральный зум
Жаль, такой вариант видео нельзя поставить на заставку в менеджер...
why are you finishing it up like that. after all, it is noticeable that this is an unnatural zoom
Of course it's unnatural. Its computer generated.
100k subs sliver button
amm eat fresh
This gives me anxiety.
Isbanat
Also, this zoom is not deepish. It is VERY deep, your third deepest zoom, in fact.