This is the best explanation of both the Mandelbrot set and complex numbers I've ever seen, great work!
@TheArtofCodeIsCool
6 жыл бұрын
aww thanks. I appreciate your appreciation :)
@expchrist
4 жыл бұрын
@@TheArtofCodeIsCool this really was an exceptional video
@radrook7584
2 жыл бұрын
These fractal patterns are evident in nature and are not just computer-generated possibilities.
@anastafah7795
5 жыл бұрын
man you are in another level in explaining, thanks so much!!!
@子维-u1g
5 жыл бұрын
Amazing, thanks for you effort master!
@arkondigital1496
Жыл бұрын
Literally Art of Code
@EmilMacko
6 жыл бұрын
This video easily deserves millions of views!
@TheArtofCodeIsCool
6 жыл бұрын
Aww thanks! You can share it with the people you know to get to the million faster ;)
@dh7222
6 жыл бұрын
thank you very much for this! really informative and well edited video!
@TheArtofCodeIsCool
6 жыл бұрын
Thanks! I'm glad you found it informative :)
@dleddy14
4 жыл бұрын
This was really good. Thanks.
@colinjava8447
5 жыл бұрын
Very good, but the explanation of i was a bit dodgy when you said the rules were different. I would have explained the need for i in solving equations like x^2 + 1 = 0, so we create a new number that's on the number line, so we get a 2D grid.
@TheArtofCodeIsCool
5 жыл бұрын
Yeah perhaps, I'm kind of figuring this out as I go as well. I'm not a mathematician.
@LaukkuBah
5 жыл бұрын
I think the real lesson here is programming before hoes
@TheArtofCodeIsCool
5 жыл бұрын
LOL
@realcygnus
6 жыл бұрын
top notch channel.......best visual explanation I've seen
@donaldviszneki8251
5 жыл бұрын
>That *was* my girlfriend
@Kizzudoramu
5 жыл бұрын
This is the absolute best explanation of fractal generation I've ever seen. The dancer metaphor was perfect. Great video, thank you.
Hello! Great video. While I watched some videos about the Mandelbrot set that delve into the mathematics (on the Numberphile channel), your analogy with the dance competition really connected everything together. Thanks!
@sacredbanana
6 жыл бұрын
I never thought I'd finally understand the Mandelbrot set today, but I did. You sir deserve a big Easter egg!
@TheArtofCodeIsCool
6 жыл бұрын
Cool! I'm glad it helped you :)
@stylis666
5 жыл бұрын
_...it goes to infinity, over there..._ Because that where infinity is and it's nowhere else, just in case you were wondering where you left it :p
@martingachagua4554
5 жыл бұрын
Whizz Stuff. You Refreshed My Coding. The Dance Floor illustration And How The Steps Could iterate Was Superb. Then You Showed How Your Computer Operated On The Variables To Create The Mandelbrot Fractal. Your Labor Was Worth It! After A Few Videos . . . . This Was The 4th, . . . . . I Feel That You Took It Home For Me. Appreciated.
@TheArtofCodeIsCool
5 жыл бұрын
I'm glad you got something out of it!
@murators4732
Ай бұрын
WOW! You explained it so well! Just subscribed. Because I watched several videos and so I just better understand how well you explained it! Couldn’t be simpler. Will watch your other videos! Just could be as good as this one! Thanks!!!
@abeljonathan7324
5 жыл бұрын
Today I found your channel, what a nice day 🙂
@oneofthesixbillion
5 жыл бұрын
Thanks, I especially appreciated 2 things. I've been confused by complex numbers and you showed how to work with them using simple algebra. Also the dancer analogy that showed how the start point affects whether the given number goes out of bounds gave me a nice conceptual understanding. I was completely confused about how the points map to colors. I didn't see any point plots or how colors are assigned to the points.
@TheArtofCodeIsCool
5 жыл бұрын
The color mapping is usually based on the number of iterations. This can be completely arbitrary. If you divide your number of iteration by the maximum number of iterations allowed, you'll get a number between 0 and 1 You can then use that number to look up a color out of a texture. The texture could hold any color gradient you want.
@studyrxyoutube
3 жыл бұрын
👁👄👁 idk why but you are dope. 🙌🏽 thanks for the video. Never even coded for anything like this besides MySpace and some practice as a hobby. Just finished your part 1 of coding The Mandelbrot and I’m going to give it a shot! 😅 I have a crappy Mac so let’s see if it even opens The program
@jhonkitri
2 жыл бұрын
Hello sir, Can you make a video tutorial for working on the Mandelbrot Set Fractal Accelerator project using the quartus and nios ii applications based on the book EMBEDDED SOPC DESIGN WITH NIOS II PROCESSOR AND VHDL EXAMPLE (Pong P. Chu Cleveland State University) on page 637?
@__hannibaal__
Жыл бұрын
In the past 20 years i try very hard to visualize a fractals by reading what’s image coding bitmap, windows API, C, C++ , and at the end I FAIL , so i abandoned totally the project but i keep studying Fractal analytically, by hand and realize very awesome results. Now when i return to programming i realize how these thing is easy.
@THE_ONLY_GOD
2 жыл бұрын
If the large US tech company I interviewed at multiple times this past calendar year or so (yes, I thankfully got the binary tree traversal coding portion correct in an interview) would ACTUALLY HIRE ME (or if I figure out how to get some good paying clients) then I could more comfortably afford to donate. Currently in another country to comfortably afford the rent and the past week or so a speck of blood appeared in the field of vision of My right eye, so hoping My situation VASTLY improves soon!!!
@FinanceLogic
8 ай бұрын
thanks. this looks good and i'll watch it closer later but you seem to understand this book so well that i hope you also read "fortune's formula" by william poundstone to make those red up and rights real. a little incerto by taleb. thanks for the vid.
@hareecionelson5875
2 жыл бұрын
it just occurred to me that, if multiplying by i is a rotation of 90 degrees (anti-clockwise), then multiplying by -1 is a rotation by 180 degrees imagine if negative numbers were explained at school in the context of rotation: it would make the jump to imaginary(terrible name) numbers a lot more intuitive, since i x i =-1, which is a total of two 90 degree rotations
@davidgb3652
16 күн бұрын
you don't know it, but I'm watching all your videos as if you were my teacher. I owe you a lot.
@THE_ONLY_GOD
2 жыл бұрын
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.
@valzugg
3 жыл бұрын
r*r=r? what is this sorcery? Very nice explanation though, the dancer metaphor helps!
@ahmedsalman17
6 жыл бұрын
Excellent video Thank you very much
@THE_ONLY_GOD
2 жыл бұрын
Would be interesting to have a particle "drum" sent from origin to bounce off the walls and every bounce make a sound...curious if that would make fibonacci sound sequences or...?
@THE_ONLY_GOD
2 жыл бұрын
Thanks! Can better explain the z equation portion of the shadertoy code? How is that z^2? Thanks in advance!
@DaRza17
6 жыл бұрын
I was kinda shocked when I saw this channel only has 2275 subs... wtf
@bbrws
5 жыл бұрын
right? this should have so many more views!!
@jhonkitri
2 жыл бұрын
Heloo sir, can you make a video about Mandelbrot set Fractal accelerator using quartus II 13.0SP ?
@THE_ONLY_GOD
2 жыл бұрын
There is a way to nest another shader in a shadertoy shader? For instance, if I wanted to have portions of a shader output colored with another shader? Thanks in advance for explaining how!
@hitman17011986
Жыл бұрын
Woww.. Never knew someone could explain it so well.. its just amazing! Thanks a ton.
@THE_ONLY_GOD
2 жыл бұрын
By the way, every branch of The Mandelbrot Set has a fibonacci number of sub-branches.
@THE_ONLY_GOD
2 жыл бұрын
Isn't "1+2i" squared -3+4i? (the 2i times 2i turns into a -4, correct?)
@chandrakanth4241
5 жыл бұрын
that thumb nail, You just nailed it for sure.
@kogorek1
5 жыл бұрын
Better explanation than professors at the university
@THE_ONLY_GOD
2 жыл бұрын
How to put a rotating raymarching object into every "orbit trap" of that fractal in Shadertoy?
@anmaral-sharif1381
6 жыл бұрын
"Like" before watch. 👍
@kebman
4 жыл бұрын
The steps explains why the computation of the Mandelbrot set becomes slower and slower as you zoom in. Isn't there a way to compartmentalize the zoomed area, so it requires less computation? Edit: isn't it just a matter of making the test area smaller?
@TheArtofCodeIsCool
4 жыл бұрын
That's a great observation. Yes, when you zoom in on an edge of the fractal what happens is that all of your dancers dance more steps before leaving the dance floor which makes the competition last longer and the frame longer to render. There is not really a way around that.
@crowdedcrow3098
3 жыл бұрын
In spite of my uncertainty that you'll see this comment, I feel compelled to blow a thousand rainbow-colored bubbles your way (such corny imagery can be blamed on my irrepressible child-like wonderment), each lovely, wet sphere a compliment to your work. Confession-time: Mathematics, as well as the subject on which you speak, is like a beautiful language constantly transforming into evermore mesmerizing shapes and textures and sounds that exist behind an impenetrable barrier I've been kicking and punching my whole life, only to end up with broken bones. I mangled two math books while attending University because I would go into fits of helpless rage and frustration; I felt entirely impotent to grasp what I sensed was forever just beyond my reach. Now I realize my ability to understand such concepts was never so close, and it remains at least 5 light-years away. I'm not proud of my mathematical/coding illiteracy, as I intimated, it's much like standing outside of a museum window, wishing I could have the painting I see hanging within. I recognize the beauty and complexity of it, even if I can't precisely translate what I'm seeing. I suspect my literary devices are fraught with tangles... probably because I'm out of my depth when I attempt to get "technical". Not only am I not able to understand math equations I'm so intimidated I screw up trying to articulate my lack of understanding. Do museums even have windows? Wouldn't that be a security risk? In any case, the gratitude bubbles were meant to illustrate my appreciation of your teaching style, your use of ballroom dancing as a metaphor, and other points I shouldn't list because I've been rambling since my second sentence. I can't claim to fully understand, but my struggle has nothing to do with your gift for making clear what wasn't. It made sense as you were explaining it, but give me five minutes and my brain is back to punching fuzzballs and kicking at nebulous clouds of incomprehension. Good times, don't try it.
@TheArtofCodeIsCool
3 жыл бұрын
While you might still be struggling with math, you certainly have a way with words. Thank you for your comment, and thank you for watching!
@davidhopkins
4 жыл бұрын
Thanks for this. The dancer analogy was really helpful. I am most appreciative that you did the hard work of explaining how you square and add complex numbers. The numberphile videos pretend to explain things but they breeze right over how this works.
@TheArtofCodeIsCool
4 жыл бұрын
Glad it was helpful!
@frankconley7630
2 жыл бұрын
Using the dancer example, when you zoom in 10 or 100 times what are you looking at. I'm flummoxed. I cant learn what the shapes are when i watch Mandelbrot zoom videos. What determines the shapes and colors around the focal point? Please respond. Anyone.
@TheArtofCodeIsCool
2 жыл бұрын
You are looking at the scores of the dancers that started at the exact locations you zoomed into. The colors are just the score, mapped to a color. You are free to turn scores into colors anyway you like. Here, I use the score to look up a color from a texture with color gradients.
@dAni-ik1hv
11 ай бұрын
tbh the dancer representation was so good a 4th grader could probably understand it
@hangli3232
3 жыл бұрын
Hi, this is probably a stupid question, but could you please tell me why 16:45, you use (r+i) to represent a point, I thought it would be ( r , i )? Or is there any resource or key words that I can search and learn this? Thank you!!
@TheArtofCodeIsCool
3 жыл бұрын
It's just how complex numbers are represented and how the math works out. You are right that in (computer graphics) vector form, it would be represented as (r, i)
@Kurtlane
3 жыл бұрын
What would happen if instead of Z = z^2 + c we have Z = 1/z + c or Z = ln(z) + c or Z = sin(z) + c etc.?
@TheArtofCodeIsCool
3 жыл бұрын
You'd get a different kind of fractal that is most likely not nearly as cool. Having said that, I encourage you to try it.
@davidhopkins
2 жыл бұрын
This is hands down the best explainer of the Mandelbrot set. Is the dance program you use available for the public? My nephew is obsessed with this stuff and I have been struggling to explain it to him. I think it would really help if he could plop down his own dancers on squares of his choosing and watch them go.
@TheArtofCodeIsCool
2 жыл бұрын
It's not available at the moment but you're not the first one to ask so I'll polish it up a bit and release it to the public.
@davidhopkins
2 жыл бұрын
@@TheArtofCodeIsCool let me know if you need a beta tester. 😉
@greggsannes493
5 жыл бұрын
I'm still learning but you give me hope thank you😊
@Nanookh54
5 жыл бұрын
Agree with fuglsnef. You make it understandable for the layman. Great work man!
@yendorelrae5476
4 жыл бұрын
"so that's...kinda how...this algorithm works" I think he is trying to explain it to himself at times
@DaRza17
6 жыл бұрын
This guy must be the genius brother of Bill Burr
@jbGraphics_
5 жыл бұрын
I've never heard the dancer analogy - this is really awesome, thank you
@alexclay7570
6 жыл бұрын
I would love to share this video on Twitter. Do you have an account there that I can credit? :)
@TheArtofCodeIsCool
6 жыл бұрын
Aww thanks! It's @The_ArtOfCode
@THE_ONLY_GOD
2 жыл бұрын
So weird that the code doesn't need any imaginary numbers maths.
@andrewg3196
4 жыл бұрын
Haha looks like the computer problems maybe came from Garbage Collection? They really kicked in as the dancers were being eliminated.
@TheArtofCodeIsCool
4 жыл бұрын
I think it had to do with writing blocks of pixels to the texture displaying the fractal. I suspect that writing hundreds of blocks at once is whats causing the slowdown.
@NBsTube
5 жыл бұрын
you are a fucking genius, this explanation of the mandelbrot set is so didactic and useful, I would love if you can at some point do a similar explanation but about the mandelbulb, of some 3D fractal, I wrapped my mind around how mandelbrot works (and I still try to understand how the julia set works, I've seen a couple of good videos about how mandelbrot, julia set, and fibonacci correlates to the other in the channel 3blue1brown) but the moment you go three dimensional my mind explodes, my dream of all times is to really understand how to generate 3D fractals with raymarching, but not as many other videos do where they just show the code, but UNDERSTANDING it, thats the part that excites me. Keep doing these amazing videos, I found you last week and I love your shader tutorials, they are both good for newbies and for intermediate shader devs and computer scientist in general, I thought I would never find a shader veteran that also loves to didactically explain his knowledge.
@TheArtofCodeIsCool
5 жыл бұрын
Wow... thanks for your nice words! The 3d fractals are on the agenda. You raise an interesting point about not just blindly copying something, but actually understanding it. Videos ideas often have to bounce through my head for a few months before I know them well enough to be able to explain them well, and not just code them.
@NBsTube
5 жыл бұрын
@@TheArtofCodeIsCool yeah definitely, I like how you introduce stuff, concept by concept, you don't go for the big fish first, you introduce concepts and knowledge in layers, each one more complex and built around the previous one, that's the best way to learn, otherwise the overdose of new information usually frustrates people.
@xminusone1
2 жыл бұрын
This what your calculator see when you divide by 0.
@wormwood6424
5 жыл бұрын
Chaos, the order of the day..
@THE_ONLY_GOD
2 жыл бұрын
An analog computer can do a perceptual infinity of iterations?
@YTMartin100
6 жыл бұрын
6:55 is fantastic using the initial points and seeing their progressions in animation tells a LOT about fractals ... can you make more of those?
@mms7146
3 жыл бұрын
great video, I wish I found your channel earlier
@sallybugs1695
4 жыл бұрын
Much appreciation i was wondering i we can we get the source code
@jeyko666
5 жыл бұрын
Top notch analogy and unity dancing video game! :)
@miadzd6698
2 жыл бұрын
Excellent and simple, thank you
@prietjepruck
Жыл бұрын
Very clear explanation. Dank je wel. :-)
@vitalyantonovas321
5 жыл бұрын
Hi man! Did you know that you have fans from Russia? We are!)
@TheArtofCodeIsCool
5 жыл бұрын
mne nravitsa! and thanks for watching :)
@ClarkPotter
Жыл бұрын
This (fractals), holography, dissipative structures (and autopoiesis), and cellular automata are most of the ingredients you need to create an evolving universe replete with consciousness. Fantastic video. Subscribed.
@peiyihou8609
7 ай бұрын
amazing, it's the best one in youtube
@thehacker7488
4 жыл бұрын
Me: Okay let's do some math homework... (goes to wikipedia) Also me: uhhh wth is this??? let's do something else first: DANCE COMPETITION!1!!1
@Egosumali
6 жыл бұрын
People like you make youtube great , such a good video, thanks man i'll be waiting your future videos
@TheArtofCodeIsCool
6 жыл бұрын
aww thanks man!
@sawdustwoodchips
3 жыл бұрын
Hi there, just stumbled across your video - the explanation was great!! - I have tried using your code in shadertoy, but I am getting lots of errors. do you have a listing of the code - I get lots of undefined. will understand if you do not want to share. all teh best!the
@icaroamorim3123
4 жыл бұрын
unfucking believable explanation!
@gauravkumar-bu6xo
4 жыл бұрын
Can you explain it in after effects please
@nameno7032
Жыл бұрын
Best dance competion i ever watch Please make more of, this kind of analogy is so much fun and easy to understand the concept behind.
@sanchit8818
Жыл бұрын
Just found this video today. I have always wondered about this but never found an explanation this good. Thanks!
@YTMartin100
6 жыл бұрын
20:06 your imaginary girlfriend?
@TheArtofCodeIsCool
6 жыл бұрын
Hahahaha, maybe ;)
@galaxyfarmer4742
4 жыл бұрын
I just wanna play the funny little show case game! plz~
@galaxyfarmer4742
4 жыл бұрын
So impressive video! For not only explaining how the mathematical stuff works, but combines it with some real interesting applications!
@godramen7104
Жыл бұрын
Absolutely brilliant explanation of the Mandelbrot Set. I always come back to this video to learn more about it. This is beautifully done.
@cebustama
4 жыл бұрын
I saw the dance hall setup you created and instantly subscribed. Amazing video and content!
@LettyK
4 жыл бұрын
The mighty Mandelbrot, your fractal reminder of the day: God left His fingerprints where no man could smuggle them: in the order of the universe revealed in mathematics ~ James White
@silvertakana3932
3 жыл бұрын
Me whenever I saw something new! 0:52
@subramanyam2699
4 жыл бұрын
Beautifully explained. Thank you much sir :) and glad to know that, math nurds too has girlfriends :D
@onaecO
Жыл бұрын
SOOOOOOOOOO cool!
@gennaroschiano8085
2 жыл бұрын
You’re the man. It took me 4 years of hard work to start understanding your basic videos. One Love!
@scatoutdebutter
3 жыл бұрын
Great job. Great explanation. This is about the fifth video I’ve watched on this and it really helps. Thanks.
@THE_ONLY_GOD
2 жыл бұрын
Bravo! That transition from maths to code was great and filled in what had been missing about that. Thanks! Truly appreciated!
@mariusirgens5555
Жыл бұрын
Superb explanation!
@prtamils
4 жыл бұрын
everybody else are explaining. You are the one Does Teaching. Thanks Mind Blown
@telecommunicationslawandre6751
2 жыл бұрын
This is an excellent addition. Thank you. Can I use it in my classes?
@TheArtofCodeIsCool
2 жыл бұрын
You mean show this video? Sure! What classes do you teach?
@telecommunicationslawandre6751
2 жыл бұрын
@@TheArtofCodeIsCool Yes, I've love to be able to record it and then include some of it in my classes. I teach Communication classes. I think I've come up with a Fractal Equation for Communication. It fits perfect. Does that make sense?
@lunafoxfire
5 жыл бұрын
Very nice explanation of the Mandelbrot set! And very cool idea to play with the rules like that to get some crazy effects
@Crazeyfor67
4 жыл бұрын
A bit over my head, but all in all I finally got an idea what's actually happening to make such deep beauty. Thanks
@davidbigras1012
2 жыл бұрын
Wow!!! Never thought I could have such a deep understanding of that set!!! You did a fantastic job!!!
@alextrollip7707
3 жыл бұрын
This was mindblowing. The comparison, example and presentation was top notch. Amazing.
@ibrozdemir
5 жыл бұрын
17:50 you can also check for that rotation and more info with this video, not that i didnt find this video awesome kzitem.info/news/bejne/p3yc2qGNjKyYoKA
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