Hidden Structures of the Mandelbrot and Julia Sets

An exploration of the correlations between the Mandelbrot Set and the Julia Sets for z^2 + c. Followed by some flybys of the full Mandelbrot/Julia structures. Finally, an attempt to show the complete 4D Mandelbrot Set..with partial success.

[@Kebabrulle4869]

>understood nothing >looked cool >thumbs up

[@proberts34]

Agreed. Same. :)

[@PopieriniS55]

for real, i like this video just cause it looks cool and has insane numbers

[@jackiedoesthings6910]

In short its probably the shape of the universe...

[@maxthexpfarmer3957]

@@jackiedoesthings6910 no

[@user-NCC-1701-D]

@@maxthexpfarmer3957 11:35 phallic universe

[@azai.mp4]

This is really cool, thank you. It also cleared up the relationship between the Mandelbrot and Julia sets for me. In the end, they're just orthogonal slices of the same 4-dimensional shape!

[@ChurchOfThought]

Azai That is the right way to put it!!

[@Psycandy]

are they? mindblowing.

[@vneckexhibition]

I still don’t understand the relationship. Help?

[@ursamajor5107]

Finally, someone who speaks English. Your work on anti-particle collisions is unparalleled.

[@webgpu]

what is the 4th parameter in the equation that can be mapped onto 4d ?

[@antivanti]

Now I just need to grow a third eye and have it offset in the 4th dimension so I can see the entire structure at once...

[@AbandonedVoid]

Technically, that wouldn't work, you would still only be seeing 3D slices of the object. You would need a 4D eye and a 4D brain, as you would suddenly gain infinite more depth perception that could only be accounted for by having a brain suitably infinite in the same way our 3D brains are necessary to see 3D space by virtue of being an infinite number of planes your brain would need to be an infinite number of 3D spaces to perceive the entire structure at once. I think people forget that if there is an existent 4th spatial dimension, then no matter how thick it is there would be infinitely more information compared to what we're used to dealing with. That's the real reason 4D thought cannot be fully grasped by us, only navigated and theorized through abstraction. We would be able to navigate a 4D world constrained to our 3D perceptions just fine fairly easily, but comprehending it on that level may be nigh-impossible.

[@AbandonedVoid]

That said, were you capable of seeing in 4D, you could go even further with the fractals. The 3D space would line up side-by-side in the same way the 2D planes do to make up a 3D object, and you wouldn't need to see an animation go through every incarnation. This structure would, again, require a 5D eye and a 5D mind to see every slice of. This doesn't solve the problem, however, there would be more ways to navigate the relationship into a 4th spatial dimension that would imply that fractals would be as confusing and transcendent in anything short of an infinite spatial dimension. As far as I'm aware, at least.

you can also get 4d depth by the time derivative of displacement on each point when using perspective and a free, 3d moving eye, like a vr controller, or mouse modes this is a living test ;) nicolasnarvaez.cl/apps/ngrid/

[@randomaccessfemale]

Or you could open your hidden third eye/chakra and view the higher dimensions directly. However, to do that, you would need to abandon your self, unravel your mind and leave your body. I guess it might be easier just to grow one...

[@blackcat5771]

@@AbandonedVoid r/woooosh

[@lawrencedoliveiro9104]

Fractals give me this incredible feeling of vertigo. If you are trying to envision what infinity looks like, this is it: falling, endlessly falling, into more and more levels of detail.

[@mark879]

And a whole new universe opens up to me. I've coded both the Mandelbrot and Julia Set before. I always thought it was beautiful. But, to see it like this. It's almost spiritual. Thanks for the video!

[@thotsaboutGod]

It is spiritual in the sense that it displays the design of an infinite mind.

[@jmiller6066]

My personal favorite is the "nebula" rendering - instead of coloring by escape/set proximity, you trace every point that escapes incrementing the points it lands on. This results in beautiful ethereal images similar to nebulas in space. It's also possible to rotate the whole 4D space along different planes, which looks incredible with the nebula-style rendering. It's unfortunately much harder to code due to iterations potentially incrementing the same output pixels, but if you get creative you can still parallelize it enough to run on a GPU.

[@brian.westersauce]

It is

[@hanntonn2]

@@thotsaboutGod And it's just a small part of it. There are an infinite number of equations that could produce such shapes, each more beautiful than the other.

[@thotsaboutGod]

@@hanntonn2 It further confirms to me the infniity of our Creator.

[@risvegliato]

This is probably the most beautiful rendering of the connections between the Mandelbrot/Julia sets I have seen. And although some commenters have complained about the loudness of the music, I think it is just right. I don't know what the music is, but if fits perfectly with the visualisation. Sounds a bit like some of Terry Riley's stuff from the 60's.

[@Radonatos]

I absolutely agree, audio perfectly enhances the trippyness and the voice was clearly understandable at any point. I blame the most likely crappy (or badly calibrated) audio equipment of most viewers. Me and an couple of friends had the opportunity to play this in the auditorium of a nearby highschool - awesome trippy experience, not least due to the sound.

[@markmurex6559]

I love the music.

[@JohnDlugosz]

Radonatos I'm watching on a Home Theater PC with sound going through high-end amp and speakers, calibrated using Denon's Audyssey Platnum. I find the music too loud and have to strain to make out what he is saying,which is detracting and annoying. Speakers are by Paradigm, known for the "correct" neutral sound rather than a particular branding sound to them, and the AVX-4000 used impulse response modeling to adjust the sound to compensate for actual speaker performance and room acoustics. So, the hypothesis of that being due to poor reproduction is not right. If anything, I might think that a large auditorium speaker might add reverb and otherwise shape the sound. Another idea is that processing such as Dolby or NeoX Surround might interfere, though I would expect no real effect on audio that is essentially mono with two identical tracks. It just puts it on the center speaker instead of the L and R, which makes voice _easier_ to understand.

[@perplexedmoth]

Strange, with my crappy laptop's builtin speakers I can hear his voice perfectly clear.

[@risvegliato]

@john dlugosz - I assume that is a piss-take? home theatre, audyssey platinum calibration, paradigm speakers, Dolby, Neox surround to listen to a youtube video? As perplexedmoth says, it sounds fine through ordinary, shitty PC speakers. The setup you describe would be fine for ultimate audiophiles listening to top-notch classical recordings, with a £50k budget...

[@pastaplatoon6184]

Are humans even allowed to be seeing this stuff?! This feels akin to pulling back the curtain of reality.

[@DylanHubbard-d1p]

Trip on DMT several times, have a breakthrough where you basically get “told”, “what?!?! How’d you get here? you shouldn’t be here for awhile?!?!” And then this entity thing whatever it may be, just makes a movement in some direction and you get zipped through spacetime where you plop back into your body and you can finally remember this dream😏…then say that again😂

[@DarthCalculus]

Electronic music and mathematical animations are a perfect pair!

[@JETJOOBOY]

William Estes Should use a programme that reverses the Graphic Equaliser to make music from The patterns... Like those old Milk Drop Visualisers in reverse!

[@MuradBeybalaev]

@@JETJOOBOY Believe me, you wouldn't wanna listen to the "music" that would produce.

[@lazertroll702]

@@MuradBeybalaev what about for synthesizing timbre? _unstable_ as the overtone decibel offset, _stable_ as the overtone series' layers? ... or vice-versa? 👂

[@MuradBeybalaev]

@@lazertroll702 Not sure I understand. Probably not qualified to answer in regards to that particular application.

[@andrasfogarasi5014]

The rendering must've been a pain.

[@axtrifonov]

András Fogarasi such 3d render can be done using volume ray casting, even in realtime if on modern gaming gpu

[@MrWorshipMe]

ax trifonov What you're talking about requires all the voxels to be precalculated.. what takes so much time in rendering fractals is the calculation of each point.

[@Kalywonkas]

Dude its the mathematical accuracy, any one of these frames would take a good few minutes to calculate on your average computer

[@hackerofawesomeness]

These images have an iteration cap and it's not too high. Also, you could use perturbation theory to speed things up a TON. Think of images that used to take months to render now taking less than an hour.

[@hackerofawesomeness]

The GPU can't represent decimals to a high enough degree for it to be utilized. Mandelbrot renders are almost always done on the CPU, although I have seen a couple of cool implementations on the GPU.

[@BenedictAFindlay]

You Sir are a genius, wizard and magician. I coded 2d Julia's and Mandelbrot's 20 years ago and believed there had to be a 4d rendering possible, but never had the computing skills to make it happen. You have fulfilled a lifetime's hope. Truly astonishing, thank you.

[@alik250]

Great, another video I have to watch 73 times to understand

[@Dolmdemon]

Please show your work so we know how you came to the answer 73

[@ca-sonne-creux]

So... Did you ubderstand it after your 73. watch?

[@picksalot1]

I had no idea that the Mandelbrot and Julia sets could be visualized in 3D. That was awesome!

[@stephenstreet1045]

WOW! Talk about down the rabbit hole.

[@timleadbetter252]

Dude just casually dropping supercomputer level simulations of every possible Julia set like it’s no biggie. Mad

[@OskarElek]

You know, the interesting thing is that the sweeps along the hyper-axes actually don't produce a chaotic behavior. I'd wager that you can find continuous 1D embeddings in there (not necessarily aligned with any of the canonical axes). That seems surprising, given the nature of the base sets, but maybe it isn't...opinions anyone? Great vid btw, somebody throw a render farm at this guy so he can render this at 4K with sufficient antialiasing!

[@lucassiccardi8764]

The correlation between the two Sets is magnifically intuitive watching this animation. Well done!

[@StarGarnet03]

I love how this feels like an 90's educational program you'd find on Clickview! Soundtrack drop when?

[@mihailazar2487]

MY GOD that was pretty much the most beautiful thing I've seen all year ... HOLY SHIT

[@benross8307]

The three dimensional structures look like muscles.

[@IncolasCopperfield]

yeah, out of pure imagination it's easy to point at where the joints would be. i'd love to have a few biologists' take on that

[@ryanfranks9441]

The way the thickness of the "Strands" was rationed out via iterating on that z axis, and moving the origin point at the same time, really made it look like something that would have evolved on earth via natural selection. Cool video for sure, probably a lot of knowledge as to how stable systems form in the real world, in these sets, but also a lot of redundancy.

[@JuancharroVlogs]

What if we are the muscles of a 4 dimentional alien?

[@ryanfranks9441]

A 4d worm with that shits universes

[@jorisboulet3619]

Yeah they do, Mathematics shows up alot in nature, that is so cool. There is a new evolving theory that might replace stringtheory its called E8 emergence, its based on the golden ratio. And for me it would make alot of sense golden ratio is everywhere..

[@Eugensson]

So MSet and JSet are essentially just two 2D projections/slices of the same 4D fractal?

[@maxthexpfarmer3957]

yes

[@emmanuelalcarazvelarde6521]

+

[@jmiller6066]

Exactly - and you can take *any* 2D or 3D slice of that object - Julia and Mandelbrot are just specific planar orientations at right angles to each other. There is more complexity than we can hope to render, but the mandelbulb rendering gives you an idea (attempts to encode some of the 4D complexity down into 3D space)

[@parasiticangel8330]

correc

[@zfloyd1627]

Too bad we are 3d creatures.

[@TheJasperlife]

Super cool. This should be shown in schools to get kids jacked up on math. If I had seen this when I was a kid, I'm sure I'd be a mathematical genius now. Instead here I am watching KZbin. I've just discovered Mandelbrot, and I love it, and my daughter just rolls her eyes at me when I watch the zooms.

[@DFYSolutions]

Thanks for the comment! The zooms are hypnotic...many hours have I spent watching zoom animations! The MSet and the disk defragger program...who needs weed when you have them to stare at for hours!!

[@minnarewers3573]

I am i have watched this stuff for years now and im only 14

[@minnarewers3573]

Damnimp ye its awesome and sometimes i feel weird when i watch this stuff. Its pretty awesome tbh

[@hackerofawesomeness]

Most people use them both...

[@laurenlewis4189]

mandelbrot videos have no business going this hard. Excellent work: the most unique and enjoyable fractal video on the internet

[@mokopa]

I've been a member of YT for as long as one might be, and it's the first time that I've both favourited and subscribed at the same time. I've been looking at Mandelbrots and Julias for even longer, and I've never seen them presented this way. Although I've known about the things that were shown, this video connected many dots and I came to know things about the knowledge I have. How splendid!

[@johnmartin6548]

this is one of the coolest things I've ever seen

[@Radonatos]

I think I've seen the true shape of the god of numbers now... Great work guys, wonderful buildup, awesome rendering and brilliant music!

[@Reversefilms]

I have 0 idea what the actual fuck is going on here

[@nNiceDreamsMadeTrue]

its comments like these we spend our waking hours on

[@mojavebrennan1375]

Great explanation from someone who obviously understands the Mandelbrot Set well enough to describe it so eloquently.

[@senateop9680]

so damn true

[@chrispierce9699]

Scrambled brain syndrome here

[@scares009]

I feel like some things could have been explained a bit better, but other than that, this video is pretty cool! It's just so hypnotizing to watch this.

[@DFYSolutions]

scares009 - I'm not sure how I could explain it further...which is why I don't think I'd ever make a decent teacher!! Perhaps I'll try and make some vids in the future to go into more detail on some of the funkier points. Thanks for the comment and thanks for watching!

[@ParadoxCircuit]

Hey man I'v watched a lot of these fractal math videos on youtube and this goes in depth into some things I'v never seen before, so I feel like you actually did a pretty damn good job considering. I understood what you were talking about with the correspondences, although for the three d part you just kinda have to sit back and watch and take your word for it. (or your graphics processor's word I guess) My main issue actually was that I think your music is a bit too loud and it overpowers your voice. Other than that I think this was dope as hell, those structures at the end are mind blowing psychedelic. I hope you make more videos on this type of thing, and I subscribed so I'll know if you do! Cheers!

[@ronjones4069]

Back years ago I wrote from scratch a program for a TI plotting calculator that would display the Mandlebrot set. At the time I had a fair understanding of the math behind it. This video blows my mind thinking about the amazingly complex computing that was done to entertain us. I would like to know more about how the computing was done. Absolutely stellar programming and huge amounts of computing time. WOW

[@cubrucessecretchanneld969]

Hey what’s up guys it’s scares here.

[@hackerofawesomeness]

I think this was made with the assumption that you know something about the Mandelbrot set, the Numberphile video has a good introductory video on it.

[@jamesbeaumont178]

"we'll zoom in a bit to get more detail" yeah good luck with that xD

[@kevinocta9716]

Wow this is interesting! For someone like me who doesn't know all the math involved, I'd LOVE to see more of these types of videos. Some more basic. Some more advanced. This channel could easily blow up if you make a few more videos like this!

[@trevoror8668]

The Julia set looks like life forms. Quiet stunning love this!

[@Sensenwerk]

Wow, I just discovered this gem. When i first started watching this I was like: Damn, nice bass, very fitting for that topic. @2:28 I was sure the music was your creation. Awesome. I love the combination of art and math, fractals are the perfect starting point for such an encounter. Very impressive work. Thanks for sharing! Makes me think if i should maybe study math.

[@pdjinne65]

It's fascinating that such simple equations can create such complex designs. That's what our world is all about.

[@TanyaSapienVintage]

this video made me brain so hard my mandelbroke

[@alexsohnrey5319]

Tanya Sapien the333 best dad joke yet

[@SlashCrash_Studios]

Niiiiice

[@ianhames2465]

Isn't it just beautiful. Thank you for sharing it with us lucky ones.

[@mattomanx77]

It almost looks like a living thing

[@1Fasterblade]

It kind of is lol

[@greengreen110]

it looks really fibery, it's like a malformed plant

[@edperry4235]

This is stunning. For me, it’s the same as watching a probe travel into deep space. I have no idea what I’m looking at but it’s beautiful!

[@Icenri]

When I was in college I wanted to prove that the generalized Mandelbrot-Julia set is connected but never got any good results. Still, this video reminds me of that early work. Much love!

[@Icenri]

Travis Law I had two complex variables, C and Z0 with Zn+1 = Zn^2 + C But I have no idea to prove if it's connected, so I presented animations that were smooth enough to pose a visual conjecture. Thanks for commenting!

[@TehMuNjA]

damn the music and level of coherence with all the animations is pretty impressive too

[@norielsylvire4097]

This is genius You could see them all at the same time in 4D

[@semplar2007]

I like the video's quick style, it has less talk and more show, just what we needed. Really enjoyable. Also, at the end, visualisations got really bizzare and fastinating, especially with this music!

[@tennohack6704]

_WOW_ So its almost like the Mandelbrot set is a cross section from above, and the Julia set is a distorted cross section from a side

[@phscience797]

Imagine being a four-dimensional-being with the possibility to see this wonderful connection in all it‘s four-dimensional glory. You could see almost everything shown in this beautiful video at once.

[@modolief]

What a stunningly awesome video! This is the most interesting four dimensional object I've ever observed. A four dimensional and infinitely convoluted object.

[@DFYSolutions]

modolief - Thank you! The structures blew me away when they first appeared on my screen...as you say, infinitely convoluted...yet mathematically beautiful! Thanks for watching!

[@mrlucmorin]

Thanks a lot for a very informative video. I’m so very thankful for video authors, like you, who can present their topics without falling into the now too common trap of trying to be a stand-up comedian (and 99% of the time failing miserably). If I could give multiple thumbs up, I would!

[@andrasfogarasi5014]

Fascinating.

[@atomicjay42]

This is one of the most incredible videos I think I might have ever seen. Thank you for helping me with my science fair project.

[@aaronanderson1484]

Me before watching: "PFFF im smart, i understand fractals... i got dis." Me after: "i have 0 fucking clue of what the hell just happened... it looked pretty tho"

[@aaronanderson1484]

Me watching the last part over again: MATH = TAFFY

[@Nohoxe]

Damn. I wish more people would understand, and implement surface visualizations. There are so many concepts that are made that much more graspable when the third dimension is introduced.

[@HarrisonMartinson]

How does this not have more views?

[@DFYSolutions]

Harrison Martinson - I think most math people figure the MSet has been thoroughly studied and nothing new is to be seen...at least that's what I was told by a math professor who I was trying to get to watch this. Oh well.... Thanks for watching!

[@HarrisonMartinson]

Most viewers aren't scientists. They don't even know what an iteration is in this context. Maybe that's the problem? They might not understand this video well enough. I don't know.

[@aaaab384]

If you don't understand what the video says, then you probably won't enjoy it any more than you'd enjoy the other millions of videos on fractals. If you understand what it says, you probably also understand how obvious it is, and that such triviality didn't deserve a video to begin with. The border line between these two sets of people is not a fractal; actually, I believe it's a very small set of moderately intelligent and easily impressed people.

[@HarrisonMartinson]

Yeah, that sounds accurate

[@TheSalami]

OKAY I JUST CAME TO THIS VIDEO ON ACCIDENT. HOW ARE YOU HERE

[@YouTubist666]

Great video. Tremendous effort. Love the music. 👍👍

[@franek_izerski]

This is how reality is created in space and time.

[@ursamajor5107]

Comments like this are how you can identify the 4-D entity tourists slumming it in our garden-variety 3-D universe.

[@catfromreddit7148]

Beautiful sentence

[@shaykraz3d]

nah fairplay i respect that idk why these 2 are so arsed about it

[@shaykraz3d]

@@RandomNameLastName811 Yes, but hes just theorising. Theres alot of links in mathmatics and other sciences. Its because the fundamental concept of things having quantity (numbers) means that alot of these things are played out in real life like ice freezing creating crystals and stuff like that and certain plants that have fractal charecteristics that form from the instructions in the DNA like an equation. It all links because the way ice forms is down to how the single atoms interact with each other or in the plants case then what kind of information is sorted in that DNA, just like the simple math equation behind mandelbrot.

[@shaykraz3d]

@@RandomNameLastName811 I would argue that the mandelbrot set may not be directly linked to Psyhics, but that it visualised the pure power of mathematics and what kind of things it can generate with just a few simple rules that could be stored in DNA or just carried out naturally due to the way atoms interact with each other when they freeze etc. idk if im making sense but thats what i think hes getting at

[@dinkledankle]

I was able to understand everything. Seeing the sets in 3D was mind-blowing to say the least.

[@FourthDerivative]

3Blue1Brown: The Attitude Era

[@jansirkia3809]

Wow, just wow what a trip this was watching! I felt like I was peeking inside the clockwork of the universe somehow, while watching it..

[@deleetiusproductions3497]

Clockwork...?

[@IvanEedle]

Nice video! A bit of pedantry: the axes on the complex plane are called Real and Imaginary, not Real and Complex. Complex numbers are made of a real part and an imaginary part, so any number that lies on the misnamed axis has no real part and is therefore not complex, but purely imaginary, hence the name imaginary axis.

[@darnorkymitz2970]

fNktn true. it depends on the frame of reference here. from the whole perspective of the relationship of the axes, it is complex, but from the perspective of the main axis, any other is imaginary except at origin.

[@bascostbudde7614]

the numbers may be complex, but they are composed of a real and an imaginary component. Hence the axes must be the real and the imaginary. A complex axis would be non-perpendicular to the real axis. That works (satisfies "independent") but is not all too practical.

[@tpat90]

Re(b*i) = 0 iff b is real Else Re(b*i) = Im(b)

[@johnnotownsend6958]

I was about to correct you but you're right, the real and imaginary axis make up the complex plane

[@imjustaguy8232]

What are you guys talking about

[@Sciguy95]

Beautiful graphics, great music, and knowledge, how could it be better?

[@fredriks5090]

And i wonder; *How Aerodynamic is the Mandelbrot Set?* If only we could 3D print it with a solid material... Someone up for the task?

[@TheClonerx]

Fredrik S you cant make a 3d print of something 4d

[@kravatapraimuu]

I was thinking the same when he was showing the 3D slices along the different axes, especially the third slice- the Julia sets that ride the Real axis. Really looks like a space ship. Makes me wonder if the technology of a species much more awake than us would actually look like this.

[@morpheusft7633]

Thats what I thought too. Could make a awesome looking spaceship with that.

[@nug700]

A space ship does not need to be aerodynamic.

[@morpheusft7633]

Very true, but it certainly looks cool.

[@DisdainforPlebs]

Wow, I can't believe I only came across this now. What a great video, beautifully put together! Bravo! I love the music too, very in sync with the graphics. Hope to see more of your work!

[@novindichar]

Anyone know the title or artist of this background music? Call me crazy, but it's kind of catchy... 😛

[@badwolf2342]

Nicholas Bernards you right. This music is soooo goooood

[@ccsleepy8342]

This gave me a better visualization of 4d objects that any other video has.

[@tzisorey]

.....Anyone else want to try putting that Mandelbrot Solid through a 3D printer? I mean... a mathematically perfect and indestructible 3D printer, 'cos ain't no physical 3D printer that could do it justice.

[@paulelephant9521]

Years ago when the mandelbrot set was the new cool thing , me and a friend made some candles in the shape of sections of the mandelbrot set, they turned out pretty sweet too! That was well before the era of 3d printers (circa 1991) so we calculated the values of an interesting looking section and then made thin balsa wood slices and stuck them together to make a 3d shape and then used modelling clay to smooth them off ( the actual true shape looked sort of like a crazy fantasy mountain , but had loads of extremely thin spikes coming off it which we had to "weather" using an algorithm on our bbc micro computer to knock of all the spikes that were too thin to model and cast in wax). Making the flipping things once we had made the mould was the tricky thing! they were just so complex and easy to damage while demoulding, but they looked pretty cool in multicouloured wax bands and the way the shape changed as the wick burned was great too. Wow I've got up to some bizarre stuff in my life!

[@IARRCSim]

If anyone wants stl files for a 3D print of a fractal, let me know. Some cases of the fractal won't be possible to 3D print because they have disconnected objects but a creative solution could work.

[@JorgeOchoaLions]

An impressive video; clear presentation and intelligent explanation. Iterated Functions are not easy to explain; parameterized iterated functions, which form classes of iterated functions, are even harder to explain. The side-by-side explanation is brilliant. Kudos!!

[@MorozovaPolina]

Hi Drew! I was so much admired with this video, that I've translated it into Russian. I've got a file with Russian subtitles and would like to send it to you so that you have good Russian subtitles. Also, I'd like to ask if it would be OK with you if I did a Russian voiceover on this video and posted it on my channel? (I don't have any yet, but am ready to open one on this occasion, with Russian translation of interesting videos like yours) there would be a link to the original there. I do not know how to send a message with file attachment in youtube and do not want to publish my e-mail address here. Is there any other option to send you the file?

[@SoftDevPhilosophy]

When I thought it can't get any better, Drew took me through amazement than astonishment and eventually left confundunded. And when I thought it can't get any better, I learned from the description that it is a "partial success". Drew... respect man... respect. Honestly as f***.

[@sivalley]

Conclusion: Mandelbrot sets are made of sea life, particularly fish. ;)

[@NonTwinBrothers]

This deserves way more views than it has

[@Lorten369]

At 13:00 would make one nice spaceship.

[@minnarewers3573]

Morty McMort ITS A FREAKING FRACTAL SPACESHIP!!!!!!!!!!!!

[@Lorten369]

Minna Rewers yup and it looks cool. But as so much els is physics and sometimes math. It might just go for a good shape. :)

[@Lorten369]

Minna Rewers I for one. Think it actually is a reeeeeeeeealy good spahe. Like is already been made from someone out there. Because they are so much smarter.

[@minnarewers3573]

Morty McMort try thinking of the fractal from the vid named Trip to center Of hybrid fractal as a fractal space station. Its pretty awesome

[@geoff7936]

Did you ever watch Andromeda? Reminded me of that ship. Maybe this is the shape of the entire Cosmos, not just an expanding sphere but having tendrils going far off from the main mass. Probably just a sci-fi dream but whatever right?

[@omegaman1971]

That's phenomenal. Awe-striking. WOW

[@hackerofawesomeness]

Beautiful video. What music is that? Also, do you have stl files for these? I'd love to 3d print the 3d slice of the mandelbrot set as shown at 12:44. I can just imagine that sitting on my desk next to my computer. I'd love that. Also, how did you render these? Did you use a certain program or did you write the code yourself?

[@ci.netproductions]

Speaking of the music, I’ve been wondering what it was for a long time to. So I might be able to help you with that part!... I’ll get the song name to you as soon as possible!

[@MuradBeybalaev]

@@ci.netproductions How'd it go? I'm interested. Many commenters seem to think it's originally composed by the author.

[@ci.netproductions]

@@MuradBeybalaev I haven’t figured it out yet... I’ve been too busy doing other things and eventually forgot... I’ll get the song name as soon as possible! (Actually this time)

[@swamihuman9395]

FANTASTIC! Thx. Always new secrets lying w/i Mandelbrot/Julia:) I've studies these objects A LOT, but this vid/explanation gives me even more insight. I will be sharing this with my math/philosophy group, the WING CIRCLE, over on Facebook...

[@hoofed]

Good vid. But the music was way too loud.

[@zebra404]

hoofed way too loud

[@azuritet3]

i agree

[@LKRaider]

Crap song too

[@eblackbrook]

Yes! It gets real distracting real fast. Not a good choice for background music.

[@deliveryman7001]

ehh, i had no problem with the music, was both good and not too loud.

[@SocksWithSandals]

What a beautiful visualisation of some serious number crunching

[@deliveryman7001]

what is the music for this. i want to know! also, amazing images!

[@novindichar]

TheMailMan IsAtYourDoor Agreed! It's actually quite catchy. But I'm a synth nut, so of course I would think it sounds good!

[@Odd_Taxi_epi04]

🎶🎵🎶🎵🎶🎵🎶🎵🎶🎵 Pathological monsters! cried the terrified mathematician Every one of them is a splinter in my eye I hate the Peano Space and the Koch Curve I fear the Cantor Ternary Set And the Sierpinski Gasket makes me want to cry And a million miles away a butterfly flapped its wings On a cold November day a man named Benoit Mandelbrot was born His disdain for pure mathematics and his unique geometrical insights Left him well equipped to face those demons down He saw that infinite complexity could be described by simple rules He used his giant brain to turn the game around And he looked below the storm and saw a vision in his head A bulbous pointy form He picked his pencil up and he wrote his secret down Take a point called Z in the complex plane Let Z1 be Z squared plus C And Z2 is Z1 squared plus C And Z3 is Z2 squared plus C and so on If the series of Z's should always stay Close to Z and never trend away That point is in the Mandelbrot Set Mandelbrot Set you're a Rorschach Test on fire You're a day-glo pterodactyl You're a heart-shaped box of springs and wire You're one badass fucking fractal And you're just in time to save the day Sweeping all our fears away You can change the world in a tiny way Mandelbrot's in heaven, at least he will be when he's dead Right now he's still alive and teaching math at Yale He gave us order out of chaos, he gave us hope where there was none And his geometry succeeds where others fail If you ever lose your way, a butterfly will flap its wings From a million miles away, a little miracle will come to take you home Just take a point called Z in the complex plane Let Z1 be Z squared plus C And Z2 is Z1 squared plus C And Z3 is Z2 squared plus C and so on If the series of Z's should always stay Close to Z and never trend away That point is in the Mandelbrot Set Mandelbrot Set you're a Rorschach Test on fire You're a day-glo pterodactyl You're a heart-shaped box of springs and wire You're one badass fucking fractal And you're just in time to save the day Sweeping all our fears away You can change the world in a tiny way And you're just in time to save the day Sweeping all our fears away You can change the world in a tiny way Go on change the world in a tiny way Come on change the world in a tiny way 🎶🎵🎶🎵🎶🎵🎶🎵🎶🎵 (sorry, I couln't resist)

[@Spikehead777]

I just began to understand the Mandelbrot set just last year after watching some complex mathematics videos, and now I see this. I... umm... just... wow. Any remains of my mind from before are now sufficiently liquefied and have turned into a pile of quantum slag.

[@cfwhitney]

Are the flashes, like the one at 17.26 part computer glitches or part of the sequence? Thanks

[@eXWoLL]

For some reason I think this will be the closest ill ever get to see a full picture of the structure of our universe. Hope that when the Golem project takes air it will be able to render an amazing Mandelbrot set

[@kedapofeng8993]

Those captions gave me a brain aneurysm

[@michaelwang1730]

This is honestly better than a profound acid trip.

[@cosmosmother3212]

The shape of the Cosmos.

[@markmurex6559]

Or the boundaries of reality itself.

[@cindercinnamon2204]

Or just an interesting bit of mathematics, a curiosity.

[@cognitivedissonance4938]

+Cinder Cinnamon Well nature does seem to take mostly spiral and fractal forms regardless of scale. Some spiral things: Hurricanes Tornado's Whirlpools Galaxy's Magnetic fields Black holes's Sound wave interference Dna LSD trip Some fractal things: Coastlines Delta's Mountainranges Tree branches Root's Bloods vessels Nervous system Ice crystals But hey it's probably just one big fucking coincidence lmfao

[@radishpineapple74]

Physics gobbledygook here: Maybe if, instead of the function being z=z^2+c, the z was replaced with the universal wavefunction of the universe, (iterated infinitely many times or maybe bound by some Planck limit or something) the function being explored in such a way such that a 3D slice represents the physical universe at some point in time. Or maybe iterations would be time. What do I know?

[@weplaywax]

No idea what you're talking about, but the music is spot on!

[@OskarElek]

The credits screen xD

[@libmitchell6371]

DamnImp you are divine mind illustrating itself and we are divine mind enjoying this uncovery. Fantastic, sublime. Thank you. EvImp

[@DaveFash]

Excellent overview of the mathematics behind the "pretty-shapes". Your analytics is amazing and your relational comparisons are genius. Just like the Mandelbrot Set has encompassed all things Julia Set, I would like you to explore what happens when C = a + bi + di' (that is when third dimension using an i-prime axis). This 3-D view seems to be the superset of all Mandelbrot Sets -- when the infinite graphic is sliced at y=0, the resultant graphic is very different than the one sliced at y=.5 ( see brief intro video at mandelfash.com ).

[@dadsonworldwide3238]

In my chemically induced hulucinatings I seen this fractal pattern and was given a strong sense this is the key to everything.i could never put it in words or understand the experience until science caught up the last decade .this is a portion of the quantum world I was shown .as if for a few brief moments I was able to see Planck size bits .lol yeah I know but I'm not a burn out head just these things stuck with me all the years since the experiences .

[@dadsonworldwide3238]

Idc what a small portion of science says and does to down play consciousness or creator/most hi/ higher power there's things on every lvl from these type of induced evidence to those I've witnessed in my daily physical world .

[@antismatic]

What's the music?

[@SoL2WhiTe5C]

Wow i'm not a mathematician or something like that. I always found the Mset really amazing, but I always thought in 2D and now this video make it pretty awesome. Now I wanna know more and more about it!! Honestly, you rock! Keep going!

[@MelindaGreen]

Very nice! I made some 3D printable versions of these a while back. See www.shapeways.com/shops/cutelyaware I truncate at the boundary between points in the set and those outside, since that's the most natural, but it's nice to see your renderings that include both, using transparency and shading.

[@sevemetalogos4788]

so elegant, poetic and inspiring! Thank you, Drew!

[@undrgun]

Please tell me what program you use for this. I have a bad computer but I want to find cool looking sets and name one

[@HarrisonMartinson]

I would like to know too, I've been trying to find a good program I can trust

[@DFYSolutions]

Thomas t - I couldn't find any program that did what I wanted to do, so I wrote the whole thing from the ground up in C/C++. Essentially, the program is something like a reverse ray-tracer. I set up a camera and a look-at point, then I shoot a ray for each of the output pixels...sampling each 3d point in virtual space about every 1/500 units. Each sample point runs the MSet/JSET iteration. When a change above a arbitrary threshold is detected from one point to the next, I change to a sample distance of around 1/1000 or higher to get decent resolution at the boundaries. If a solid (aka 'inside') point is reached, the ray stops. Otherwise, it continues to sample along the ray for a set distance before stopping. Finally, it takes all the point results from the samples along the ray, assigns whatever colors I want, and merges them together via a tweaked weighted averaging. Then it moves to the next pixel!! Actually, because of low/hi sampling rate switching, and since the code is written just for this purpose, it ends up being fairly zippy...usually less than a minute per frame. I used a few different computers to generate all the frames for this video...some high end vps's, and some ancient low end machines. (The code is just doing math, so it cross compiles on linux/windows/whatever.) If there's enough interest in this, I could try and make the code a bit more user-friendly and open source it or something. Anyway, thanks for watching!

[@leyasep5919]

More videos would be cool too :-)

[@jmm1233]

Mandelbulber is good open source version if you're looking to make mandelbots and julia sets in 3d

[@hackerofawesomeness]

I'd love to see the code, even if it isn't easily readable. I'm working on a mandelbrot renderer myself, and I'd love to see some cool methods of calculations that people have done not only with the normal mandelbrot set but with other methods as well. I'm also writing in in C++ :P

[@unfinishedbusiness4088]

Love it. This correlation helped me more than most 3d or 4d videos of the mandelbrot did.

[@Illu07]

Dann maths, you beautiful.

[@tahnzahnmacmanor7291]

You sir, are a kind and loving God. Thank you so much for this video!!!!

[@Sool101]

The amount of work you put into this is amazing thank you.

[@WalterLarsLee]

Great vid. The music is a bit loud though.

[@delofon]

Woah, some structures are really nice spaceship designs. Gotta note that.

[@MrAlRats]

It's not called the "complex axis". It's called the "imaginary axis".

[@ragenFOX]

Al Rats its not imaginary if it does exist.

[@MrAlRats]

That's just what it's called. There's nothing irrational about real numbers which cannot be expressed as a ratio of two integers; they are simply called "irrational numbers". Likewise, ordered pairs of "real numbers" obeying certain arithmetic rules are called "complex numbers". Complex numbers have a "real" part and an "imaginary" part; just like rational numbers have a "numerator" and a "denominator". The Complex plane consists of a "real axis" and an "imaginary axis".

[@zzasdfwas]

While I've long known about the connection between the Mandelbrot and Julia sets, I've never seen a good visualization of the 4D structure. This is about as good as it gets without VR.

[@Pengochan]

Why is it all drowned in Noise?

[@OskarElek]

Welcome to rendering fractals buddy. Antialiasing gets very difficult when you're plotting a chaotic, non-continuous function.

[@Pengochan]

No, i mean the sound.

[@OskarElek]

Oh, I see. No idea then.

[@flyboy61699]

I discovered the whole offset thing on my own about the same time this video came out! I'm going to be writing a research paper on it very soon!

[@aaaab384]

You mean you discovered that you can cut a 4-dimensional set in two different directions? Wow, that's some discovery! Let me know when you discover hot water too, because I need to cook some pasta.

[@DFYSolutions]

Sounds cool! Post a link when it's done! I wanted to work up a paper myself, but just decided it was easier to make this (I suck at writing things down!)

[@FAB1150]

I'm so confused right now.