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MUSIC BY 6884! Check him out here: 6884.bandcamp....
The soundtrack from this video will be available on his bandcamp soon, so go follow him to make sure you don’t miss it!
I know I promised you a lambda calculus video- In fact, the video is done, but 6884 is having a field day on the sound effects as we speak, and they are coming out just as sick as this video did. Don't worry, your half-hour saga of animated tromp diagram beta reductions is on its way :D
Rendered with SwapTube! github.com/2sw...
Technical deets for the nerds:
First of all, I am using a simple escape-time algorithm with a bailout at radius 256. I understand that this approach is, in some sense, inappropriate at revealing structure in mandelbrot sets for negative real exponents, since divergence towards infinity is not expected. I have no reason to suspect it would behave either for, as example, complex exponents with negative real part. If you pay attention during the X-Set tour, you can generally see a difference in behavior on the left and right side of the screen, and I figure this is the reason, since the left side corresponds to negative real values. There are alternative strategies for dealing with things like this, such as using the Lyapunov exponent to check for chaotic or periodic behavior, but I opted to go with the simpler and more familiar approach to rendering. After all, I didn't want to taint the positive-real-part results with an approach designed for the negatives.
Another fun little quirk that I ran into here- the standard approach to anti-aliasing the color involves determining the distance that a point gets from the bailout radius after achieving bailout. This method requires knowledge of exponent- you expect greater "jumps" as the exponent gets bigger. On the flipside though, as the exponent approaches 1 from above, this approach produces noisy behavior (and below 1 it simply doesn't work.) So, if you pay close attention, you will notice I smoothly transition between gradation and non-gradation up to the parameterized value which I'm plotting in the video :)
I am also wondering what's up with the stripey behavior for some cross-sections of the X-Set. I unfortunately have not gotten around to investigating, but my best guess is that it has something to do with branch cuts on the complex natural logarithm (as used to compute complex exponentiation.)
You know the left-pointing "needle" of the mandelbrot set? During all my transitions between the X-Set and Mandelbrot set, for example at 00:42, try and find the shape in the X-Set that transforms into the needle. Notice anything interesting? :)
If you have any references about this set, let me know!
STOP MOVING THROUGH THE SIXTH DIMENSION MY BRAIN CAN’T TAKE IT
yes you will
Your brain _will_ be taken through the 6th dimension and you’re going to *_like it._*
DRINK THIS SPACE ALCOHOL AND JOURNY WITH ME TO THE SIXTH DIMENSION!
I have a very basic understanding of math and this is way out if my ballpark.
When imaginairy numbers were taught I threw in the towel.
@@ijriccanme that one time i smoked dmt
The deepest dream to be able to visualize this as a three dimensional object.
Sounds like you've never installed MB3D or Mandelbulber
Or visions of chaos
make z and c parameters, I think that would work
Edit: I was wrong in many ways about this
oh well
maybe making Re(z),Im(z), and Re(c) dimensions and so that it’s “complete”, Im(c) time would work?
(edited) wait, you can NOT just split the 1 6D shape into 3 2D shapes actually
Why to dream of three when you can dream of four, why to dream of the possible when you can dream of the impossible?
6884 did some genius music work here
Generic beep boop so good on my Adderall brain hurr durr.
@@Goodalia619 YESSS my first hater!!! 🙌
50% inspiration, 50% perspiration, 100% reason to remember the name - or however that one went 🤔
@@6884 Congrats! 🎉 I'm sure there will be many more! 🥰
@@6884as a synth head i found it really tasteful gg
The FX on the music that plays when the mandlebrot morphs - rapidly twisting the Delay knob of a reverb plugin to get that stutter - is a fucking genius use of the effect. Hats off
🧙♂️
@@6884
Where are you going after you die?
What happens next? Have you ever thought about that?
Repent today and give your life to Jesus Christ to obtain eternal salvation. Tomorrow may be too late my brethen😢.
Hebrews 9:27 says "And as it is appointed unto man once to die, but after that the judgement
@@JesusPlsSaveMe silence, brand.
i find the fact the bot targetted 6884 themself really funny for some reason
@@JesusPlsSaveMe His name wasn't even Jesus, dumbass. It was Yeshua.
Fond memories of that one 90s screen saver that would slowly zoom in on random part of the Mandlebrot set, subject to a few decades of Moore's Law. Incredible work; thank you for it.
I just want to bring attention to the fact that the music effects are synchronized with the visuals, and that makes this video so much better than anything else I've seen about fractals.
I'm guessing the pitch amplitude was factored to the brightness of pixel. Dark blue = low pitches, white = high pitches, black = quiet. If I was going to guess, those relative pitch volumes would be normalized to a reference point of the appearance of the standard Mandelbrot set, right?
@@Phriedah hehehe close enough :) just to be clear, every single automation to every single effect or synth parameter was drawn by hand because I hate myself with the fury of a thousand suns 🥰 but yes, I opened and closed a low pass filter, amongst the other things,according to how jagged was the main part of the fractal (i know it’s infinitely jagged anyways but you know what i mean). But there’s no precise, “scientific” mapping.. it’s always important to keep a human touch! (Although we are planning to automate such things a bit more for next videos, fingers crossed)
@@6884thank mr 6884 the music was wonderful
I noticed that too but at some point I was really immersed and it was just very interesting.
truly
5:28 ah yes, the suburban map set
I want AAAA Suburban home!
@@jaimedeleon1194
*Revelation 3:20*
Behold, I stand at the door, and knock: if any man hear my voice, and open the door, I will come in to him, and will sup with him, and he with me.
HEY THERE 🤗 JESUS IS CALLING YOU TODAY. Turn away from your sins, confess, forsake them and live the victorious life. God bless.
*Revelation 22:12-14*
And, behold, I come quickly; and my reward is with me, to give every man according as his work shall be.
I am Alpha and Omega, the beginning and the end, the first and the last.
Blessed are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city.
only 1 reply?
5:31 the fractals have eyes
@@Shotgunspixie That's the pi from @3Blue1Brown
I think more TH-cam videos should be like this. The immersion of the music pairing with the visuals makes this an experience like no other!
This video sure was the real official canon to everything about the mandelbrot set
woah its voxeldoesart i sure hope nothing happens to the *thing* in this video
here, the *thing* is the mandelbrot set
os c
There are 100s of 1000s of these videos in this site. What are you talking about dude.
I barely know what a mandelbrot is, or what was going on in this video, but man, it was done so well. The music, the QUALITY of this video is like better than anything i've seen. Insane stuff
This production is an instant subscribe
this guy went from connect 4 strategy to the most beautiful math video ever created.
literally
holy shit it's this guy?
@@akasakasvault7597 I need to know who this is now
I'd say Animation Vs Math is a close second.
Wait he's the connect 4 guy too??? A true TH-cam savant imo
AHHHHHHH MY BRAINS HURTS
Every day I grow sadder that we don’t exist in higher dimensional space because of how much beauty there is in higher dimensional math
U will be able to access that once u die and join God in his glory
Reading Greg Egan's Diaspora will either make you much sadder or give you some solace as read about the higher-dimension travels of the characters.
Blood doesn't know its fingers lmfao
But we do -- we just have trouble perceiving it :-)
@@gracetonsanthmayor6687 what if there is no god
As a person who used to develop programs making Mandelbrot sets and other fractal renderings in the early 90s, I know first hand how incredibly CPU/GPU intensive these animations are compared to back then. For perspective a single frame of 640x480 pixels with 16 colors on my Intel 386sx 20MHz from 1991 would take 4 hours or so to render. Granted back then if I had a math coprocessor it would have been much faster even then but this rendering here is thousands of times more complex and animated! I’m not sure this could have been calculated in a life time on the old system. How far we have come! Great video
He explained it so clearly and elegantly as well.
I had the Mandelbrot algorithm in BASIC which I would try on various systems. 1st was a Sinclair QL which took 24 hours to draw a whole Mandelbrot set in 512x256 4 colours, 8 hours running the algorithm in compiled Pascal. Then there was my Epson PX-8 running the algorithm in Microsoft BASIC on its 640x64 mono screen. That also took a day just to generate a 64x64 low res set. Then there was the Acorn A3000, a RISC based system running BBC basic on the forerunner to the ARM processors we all use today. That same algorithm generated the set in 640x256, 256 colours in a little less than 4 hours. Beyond that I had discovered Fractint on PC which generated a set in an instant.
A complicated comment about a complicated thing which makes sense?! A rare sight to see!
@@zapod20 Damn, I've gotta check that out! Does Fractint cost anything?
thousands? more like billions
7:26 This is happening because the shape keeps getting put at right angles to itself. Pretty fantastic. The 6D shape was something else.
oh my god, man, the audiovisuals.... I wasn't prepared for music frequency filter parameters to change with the parameters on the screen. thats such a great touch
Yes, the music is genius, but let's draw attention to the incredibly timed bitcrush effects on the narration. Just an incredible move to make the narrator feel like they're fractalizing away.
idk i kinda thought it was just distracting to me
it's like ur brains on ket
@@6884probably the best sounding brain melt I've ever experienced. I'm returning to listen while high for extra entertainment later haha!
@@vii-ka how
it was fucking incredible
This is the first time I've ever had an intuitive understanding of the Mandelbrot set. Excellent video
Bro watch any Numberphile or 3blue1brown video on it. There are several.
Yeah the explanation of how to visualise the set was amazingly concise!
It's just a color coded coordinate system 🤯
i had no idea what a fractal /was/... i knew they were math related but thats it. this video didnt even need to explain it. wow
the sound design on this is amazing, really well thought out, it really makes the video really rich. the point tracking sound design bit at 4:20 really was super cool. I think you really pulled of some amazing work here. very well crafted.
@ beautiful work.
Mind had exploded by 0:45
dude the sound design is insane. don't get me wrong, the visuals are wonderfully smooth and endlessly enjoyable, the explanation was crystal clear, but I've never seen a YT explainer with such an immaculate sound design!
I love how your voice gets the sudden reverb, or undersampled and bitcrushed when showing the simpler visualizations, how the music gets a whole bunch of crazy phasing and different elements fade in and out when moving around 6D space.
I loved gravity basins but I somehow missed the sound design. you two collaborate so well, I really feel like there was thought and preplanning put into how everything melds together
Note that raising a number to a non-integer power doesn't behave as good.
For instance, for the power of 1/2 you get the square root, which will have two regular branches, meaning you will have to decide arbitrarily which one to pick. And when you smoothly change the input the output doesnz't change smoothly at some seam (which also can be chosen somewhat arbitrarily), so technically you have to choose one of 2 "equally likely" variants for each next point
For a power of 1/3 there are 3 options
And for an irrational power... infinite options, in a sense
So that's my best guess for why this fractal is less well-known and studied (and less well-defined)
Has amyone ever thought to square or cube both z and c together and see ifnthst gives any new insight? Is that a clever and insightful idea on my lart pr that has been done already? Or change one pf them toma fibonacci number or swuare both and THEN add a constant? Just spit balling...
@leif1075 you would end up with the following:
z0 = c0
c1 = c0^2
z1 = z0^2+c1 = 2c0^2
so, it would behave like zn = 2^n c0^(2n)
which does not seem interesting, because it's just (2sqrt(c0))^n
however there's probably something to be done with cubing c
or adding w = w^2 + z for recalculation and plotting w instead
there are actually a lot of fractals on recursive formulas in polynomials and I suspect that chaning c or adding w might be expressed in a form of just one variable with polynomail recursive relationship, but who can say for sure
Uhhhhhh Taylor expansion would have a word with you...
@@Neuroszima convergence radius of Taylor expansion can be finite, can it not?
Particularly, if you're getting a Taylor expansion of a function it converges on some disk centered around the point where you're getting your expansion from, the Taylor expansion is regular and only equals to the function when it is regular in the disk as well. Square root is not regular at the origin, so the Taylor expansion would only converge on a disk that does not contain 0.
That exact mechanism that makes the plot look incomplete at some spots for example when he shows the 3.5 exponent c-parametrized fractal. It looks like if you broke glass and attempted to put it back together. The only way to resolve those seams is to add another dimension to showcase those branches.
P.S. I imagine a method similar to Veritasiums "Logistic Map" video except the extra branches are show above and below the principal branch.
Shoutout to 6884 for making the video 50x better
Eyyyy cmon cmon i just uncovered its beauty in… hehe, in another dimension 😉😊
you mean 50x+2i, surely 😄
? what y mean 6884
@@NoNoahhhh itsa me
@NoNoahhhh 7:36
Mooom help, this guy is warping space and time
Mom said it is my turn to ponder the imponderable!!!
Moooom! Phineas and Ferb are warping space time!
Hey I just wanted to say THANK YOU for both making an engaging and educational video (I legit feel like Im looking at universes converge across a plane or something) but for also including the tools you used and the technical information. I think most people are capable of learning about these things on their own, but so so often creators will drop an amazing video and never reveal what tools they used or an entry point that we can use to learn more about the topic on our own... and that can be frustrating. So, thank you!
3:00 Manipulating the starting value and seeing the effects in real time genuinely blew my mind 😮
Exquisite sound design, narration and use of math. Perfect fractal video.
This is INSANELY cool. I've never considered making the exponent an imaginary number, and the music really ties it all together. Nice!
the music reminds me of the way the music changed when rotating in 4-space in 4D golf
Absolutely! Also considering that this video is too sort of about making cuts of a multidimensional space
What 4d golf? :0
@@JuiceboxSnail It's a PC game made by CodeParade, really recommend checking its devlogs and (if you like golf of couse) the game itself too
@@JuiceboxSnail It's a PC game, really recommend checking its devlogs and (if you like golf of couse) the game itself too
ohh i didn't know the game but you have my curiosity now
Bro, this music and sound effects are amazing
This video is mind-blowing! What the hell this is great! the scoring is insane, and the explanations are better than I've seen before. Incredible
My god, as a misician i want to express how MUCH i love your sounds choise and how it changes with yhe visual, it is so impressive.. ive never seen anyone doing that and so good!!!! I am very impressed!
hi :3
@@6884 can you tell me the name of the music?
@@vaiyaktikasolarbeam1906 ah hello again! well there's no real name because I composed the whole thing specifically as a soundtrack for the video
@@6884 ah then can you upload the music separately? Please?
Nice work with soundtrack, 6884!!! 🌌 Relay my thanks.
my thanks back!
@@6884 can you upload the music?
@@6884 You never had to make such awesome music but you did. Did you make this song just for this video in collaboration with 2swap?
@@KawaiiFlandre495 if I could, in a sense I also had to :) I was in a moral obligation with the universe to make something good to go together with something as amazing as the visuals!
I absolutely love how the music and sound effects change with the fractal
At 6:20 feels like a toby fox background for the secret boss.
The sound design and composition of this video is mind blowing. What an incredible level of polish! Careful attention paid to each and every detail, wow
Dziękuję, ale niestety jestem tylko Włochem
the sound design in this video is amazing, and it's super interesting! Please keep doing what ur doing, it's super awesome and u totally deserve more views! props to 6884 also!
The sound design is phenomenal
thanks :)))
you did a good job 6884
As a youngster, I wrote a C program that displayed any 2d cross section of the "mandeljulia" 4d shape. If only I had even thought of fiddeling with the "non-variable" 2 as well!
Interesting video, subscribed.
The way the music shapes around the visuals is absolutely mesmerizing, what a demonstration!
as a musician/sound designer, this is one of the coolest usages of sound design i've ever heard. 6884 is a sound design genius
*blush*
Goated video. Been playing around with mandela browser and fractals we can see are just a small window into a kaleidoscope of high dimensional complex math.
I fucking love the sound design here, also FRACTAAAAALS!!!
one of the most underrated math channels on youtube, great explanations and visuals, and the sound design, especially the music being synced with the visuals, made it so much cooler. keep it up❤
truly amazing animations and beautiful visualizations
may the algorithm bless you 🙏
@6884 deserves a Grammy for the sound design.The choices you made are so intuitive, and seem to accurately reflect the ambient resonance of these forms and how they might sound in motion. The levels of detail that you modulated your effects to correspond to the visuals is mind blowing. You made very obviously synthesized sounds seem organic as if it's an analog recording of actual physical objects moving in a substrate. I know my way around electronic music production and it's very clear you do too. This is phenomenal work and you should be very proud of what you've acheived with this video.
Because of sounds and visuals I thought that you have at least 300 000 subscribers. Nice work
such an insane video, absolutely love the sound design, visual design and how everything works together to make just a phenomenal video
It takes a witch to recognize some magic 😉
This is just amazing work, and I'm just surprised at how underrated your channel is. the music goes great with it. I also like looking at other fractals you can get by iterating other functions (Burning ship, Tricorn, etc.)
Never have I been this entertained by a video explaining the Mandelbrot set. Astonishingly beautiful.
The way the music effects get modulated with the visuals of the mandelbrot was very cool and engaging. I'll definitely check out 6884's stuff.
logo checks out
I mean profile picture. I am sleepy.
I was very happy to be connected to my speakers when i heard this music. Hats off to 6884, very immersive
best video ever, best content creator ever, love the raw appreciation for fractals
my favourite ost ever btw
This is awesome 👏
your music guy needs a raise
The music and the vocal changes are just so good! You and 6884 are so talented!
😎
@@6884 I could fall asleep to this masterpiece bro :D
I just gave this whole video my undivided attention from start to finish. And I have absolutely no idea what it was about. However, I genuinely loved it.
I can't believe this has only 1500 views. Incredible work. I hope you find great success on TH-cam soon.
the main star of the show is the math, but the sound design also deserves some praise. well done man
Wow, this is absolutely phenomenal in every way. This should be trending among the top videos of all time, undoubtedly.
The sound design around 4:05 is great! Really nice touch!
holy cow amazing video its the best fractal video ive ever seen and it finally made me understand how drawing the mandelbrot works
Probably just the minds inclination to pattern recognition, but I saw lots of familiar things in these animations; burn paths from electrical archs, in the 3rd dimension cosmic filaments and their clusters, 5:58 literally looks like the flower of a protea - the colour intesity towards the peak and the secondary set of petals.
Again, just sharing my account, but speaks volume to the universe's fractal nature.
0:29 youtube compression at it's max 💀
Also TH-cam: this video is 4k ultra resolution , one of the best on TH-cam
Average fever dream
Visuals, sound, narration are amazing. 10/10 video
The music and voice changing with the video were a genius move
Unsolicited potato at 2:32
Lol
Absolutely disgusting and horrifying. Thank you for your amazing work and video! Im petrified of fractals...
7:31 the singularity forms
crazy how you did a math video in the form of a true crime documentary, i usually save to watch later but the insane quality made me watch right now.
one of the coolest videos ive seen… especially with that sick music
GOBT DANG IT IS A CAT WIT AN HAT
5:15 Best part
And *THATS* how you fold reality! 👏
🤣
0:19 hey my name is Julia:D
yooooo me too!!! :D
That’s what they want you to believe
lol
👍k
Slide me your number
I'm guessing there's really just some sort of self-similar 6-dimensional structure that we can only see slices of. Very cool visualization. I like the rotation of the viewing plane.
althoug some humans are working on getting us closer 😉 look for 4D Miner and 4D Golf. Crazy stuff and some kids already play it like it's nothing.
THE most elegant, straight forward explanation of the mandelbrot sets i've ever seen. Not to mention the incredible music/sound design. Thank you
the part where you made the exponent a non integer literally gave me a chill. Numbers have forms that we cannot comprehend but are intuitive when you show this.
7:00 Absolutely. The relationship between these two really, is that Mandelbrot is a tourist map of c values of Julia. Picking somewhere close to the border will give you something interesting-looking. And, a small neighbourhood around the origin of one plot will look quite similar to the same neighbourhood of the other.
Looks like Eldritch horror.
something scary about this is that at around 6:40 or so, you can feel like you're zooming in through a 3D corridor of sorts. it has perspective. thats somewhat spooky.
This is the first time i've actually _understood_ someone explaining the Mandelbrot set! Great job!
I love this video! The visuals are great, but the beautiful audio design makes this feel so so so much more alluring and amazing. This honestly feels like trekking in alien space/higher dimensions seeing these fractals change and morph. Am honestly stunned. Wow!!
3:26 Ukraine founded
lol😂
The immersive experience given by the visuals and music is just so stunning.
The breakcore drums at 4:06 works so well; the seamless transition between topics and visuals; the efforts put into the voice filtering throughout the whole video… It’s just so wonderful to see such well made piece of art.
I’ve long known the beauty of the Mandelbrot and the Julia set, but your work again reminds me of how beautiful math, and the world, is.
A slight pity, though, is not mentioning about the relation between the “number of convergent points” and the “blob” the initial point falls into. The usual Mandelbrot set (z=0, c=2) has such phenomenon, but I’m not certain if other sets in the family have similar properties.
maybe ill talk to this sone day :)
"breakcore drums" 🙄 jfc
5:17 kinda looks like the pov of someone being crushed by portals in the portal game
Anyways cool vid
That was amazing. PLEASE do more of this content.
We've all seen fractals and once you've seen a couple videos zoomng in and out it loses its novelty real fast. And it's like, yeah ok, we've seen this before. Even artists like Julius Horsthius, whose work is phenomenal, suffers from this same kind of novel event horizon, where you only need to see a few examples before it all starts feeling like more of the same.
But you just showed us something new, using the same old fractals. Please explore further, this is very exciting.
thank youuuu 😭😭
I heartily concur with this comment. BEAUTIFUL combination of motion and sound!
Sometimes I think I’m a pretty smart guy and then I see stuff like this and realize just how smooth the ol frontal lobes really are.
5:08 Corrupted Minecraft world generation be like:
Feels like 2010s TH-cam, super creative and entertaining, yet educational.
I _wishhhh_ I were able to percieve 4 or even 6 dimensions natively
4 isn't so hard to visualize, though the only case which is really intuitive would be space-time where you can imagine yourself as something like a worm connecting you when you were conceived to when you pass away.
Each slice is defined by a position and a time. You are just one slice of a long worm in space time.
There is also an old video on how to visualize 10 dimensions you can check out.
May I suggest lsd or dmt?
@@isaackellogg3493so true😂
I suppose for the 30th dimension, you'd _wishhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh_ it.
That was the most captivating and straightforward walkthrough of fractal math I have ever seen. I've played with the formula a fair bit but never put together the various still images that were generated. Putting them into motion and showing the connectedness between the various parameters was really fun to watch. Thanks!
this is by far the best fractal video I have ever watched. the music, the visuals, the explanations. perfect.
Playing with fractional exponents gets a little dicey, doesn't it? You have to settle on a specific branch of a Riemannian manifold (if I have my terms correct). This is why the fractional exponent examples have all those hard edges.
That's why it's an *evil* twin
yep
Oooooh right!!!! 😮
3:13 from this point on I am confused
The music warping is funny here 4:12
The music choice was absolutely perfect. Thanks for this video.
thanks for this comment!
I feel like the music is a wonderful sonification of what is visually happening - in the same way that data points falling into the mandelbrot set can be interpreted visually as this amazing fractal character - the music is creating an audio interpretation of the math and a narrative of the math by the artist. Big up 6884!
aaand its all over the screen
been there, keep the tissues at hand ç__ç
And at 5:35, it even shows pi!
You sound like 3blue1brown
Bro IS 3blue1brown 2nd channel.
Instant Sub! Sick video! :D
The music was out of this world. Fit perfectly.