I am always impressed about how you manage to create complex programs without ever defining proper functions, which you clearly dislike :-) Awesome job!
28:00 I was holding my breath, crossing my fingers, and rooting for you. We really really appreciate the hours and hours you spend...to put together these incredible videos. You're the best Dan!
I remember the video on the Mandelbrot from 6 years ago .. back then I was in high school .. it was around the time when I just discovered the channel and I really loved your content .. my whole family knows about you because I couldn't shut up or stop watching your live streams and videos I remember also sending the video to my Math teacher and he was truly impressed even though english is not our native language Man .. I just realised how much you taught me in coding Thank you 🙏🙏❤️
THIS IS SICK! I've been obsessed with mandelbrot and buddhabrot fractals for YEARS because of your video on the mandelbrot set. I would LOVE to watch a video on ray marching and shaders!!
This video is what brought Processing (and your channel) to my attention. Currently finishing your NOC series and planning to learn p5.js next. Thank you old and future Dan! Edit: to clarify, I knew of your channel years ago, but I lacked the experience and motivation to watch your videos, and didn't know you had such amazing tutorials!
Dan, I love to see a new video from you. I am a senior software eng. working in the business for the past 20 years. I love the humanity you bring, along with the self deprecation and humour. I trust Mrs. Gloria Pickle is doing well:) Now to sit down with a cuppa and enjoy this. Thanks again - from Ireland.
Love your content and the way you are teaching the subjects. One hint to improve your code further (starting 22:50 ): when the edge is set to false you have to add the previous point to the mandelbulb array. What you did was adding then the next point in the line. Because it is a fractal there is a high chance you hit a whole and the next "edge start" will be added but you are missing almost half the points. "Almost" because on one pixel thin "edge switches" you just got it correct
Awesome video, I have been into fractals for almost a decade and this was one of the most accessible explanations and implementations of the Mandelbulb I have seen.
The best about the videos is neither the cool outcome nor the educational purpose, but rather seeing how much you love coding. It's so sad how often education fails, just because it seems like the one teaching is not even enjoying it themselves, but this enthusiasm is very infecting :D
I've learnt more from this guy than I have in all my years of school and college, and the best part is how much fun it is. I would be an Einstein if I had a teacher like you.
This was awesome from start to finish! Really shows the thought process before jumping into coding and of course all the naunces of jumping back and forth! Good job!
Finally waited long for this one dan , thanks for the delivery you chered up a little neighborhood in Bosnia (south europe) much love as always the magic and long train of coding
So crazy you came out with this. The last week I've been obsessed with the Mandelbrot set and coding it and was exploring the idea of 3d this is very cool.
Okay that does it. I have no reason in my field to learn these animations but after watching you have so much fun I'm going to learn JS and processing. I have to board the train. Wish me luck!
I just found your channel last week, and have just been enjoying these challenges videos. I was having a bad day today but after watching you so enthusiastically solve and explain coding challenge just made me feel a little better. Thanks
It's great how you make code and maths look easy and pretty fun! I'm following your first tutirials of Processing and NOC and thanks to them I did a lot of progress. Thanks Daniel!
I love how your future self interrupts/intercepts the video to point out issues with the code and/or explanations given. They way you do this in post production is just really great editing in my opinion. It just shows how much quality your videos have and how great of a teacher you are. Please keep up the great work. Thank you. Forgot one thing: as a beard guy myself, I gotta say: nice beard. I am jealous. 😂
NO WAY. I've read a thing talking about this before! Also just encountered it in a game I just finished (manifold garden). Never found out how to do it... UNTIL NOW! YEEEEESSSS thank you very much :D
you appear in my feed randomly,,i seriously dont understand any stuff about coding and never tried to learn...but the way you teach its really interesting.....i might give a shot and try to learn coding it looks interesting....thank you
Just stumbled across you channel and am thoroughly enjoying it! I am getting really strong Cliff Stoll vibes from you, and I could listen to him for dayyys. I made a quaternion raytracer between school and uni (that was around 2002/3) just because fractals fascinated me enough to dig into all that math on my own, which really wasn't easy at that time with only the limited ressources on the web then. Complete with self-shadowing and reflection maps, and a marching-cubes based mesh export for funsies as well to feed it into a "real" raytracer. It even included a fully self-made quaternion formula parser (in assembler, wich I hadn't ever used before, and support for variables to avoid re-parsing every iteration) with all the trig functions and stuff so that I could feed it all kinds of iteration instructions by just writing out a formula in text. Later ported it to an "early GPGPU style" form, under DX9 before any of the actual GPGPU stuff like CUDA and such existed. So just bare pixel shaders. I think I've never been this proud of any program I made ever since. Man, to have that kind of free time again, sigh! I never really got deep into the Mandelbulb maths-wise since it "came out" when I was already caught up in studies and work, so I followed this video with great interest and finally, after all these years, understand how it's actually calculated! Thanks! Edit: Heh, I've just noticed this video came out just one day before my 40th birthday. How fitting :)
The part where you compared the code and the white board was really helpful in understanding it. Please do it more in other complex algorithms like this
hey, from the future here lol you can take that rendered mandelbulb and save it as an image, and use disco diffusion or stable diffusion to create an image using that image as a mask! this is so amazing, wondering how this could work in python!
A really nice visualization is also how quickly the points spiral away. For that you ramp up the iterations and depending on how many iterations it takes to reach your boundary (should be r>2), you color the vertex differently. For example if your max iterations is 256, then if your tested point spirals away in 5 iterations, then you color it in some way, and if it takes 200 iterations before it grows bigger than 2, you color it another way. Anything that takes more than your limit should be considered part of the set
Just caught up with your older videos and I gotta say your coding challenges have gotten significantly better over the years. Mainly in *how* you do them. You no longer limit yourself to 10 minutes, you explain what each individual code line does and you're generally much more comprehensible for people who aren't that well-versed in coding. Way to go Daniel, You're awesome :)
Been a java developer for 13 years (recently moved to Node.js though), Anyway, usually these kind of videos are in Python, which makes it a steep learning curve for me. I'm so happy to see something that I can actually run myself, and understand to some degree. Amazing job ! :-)
You said that C gets replaced and then reinserted into z. That is incorrect, and I'm surprised no-one else caught that! The algorithm is that Z(i+1) = Z(i)^2 + c.
That was awesome. I just wanna add a bit more to the Mandelbrot set. It's story is more closely related to the Julia sets, these are obtained by iterating complex polynomials (z^2+C) and taking all the points that behave chaotically, and the Mandelbrot set consists of all those points for which the corresponding Julia set is in one connected piece. Turns out that checking the condition that you're using guarantees connectedness of the Julia set and therefore allows you to know if that "C" is in the Mandelbrot set.
I asked ChatGPT to use the Mandelbrot set fractal and an external singularity to that fractal to create a set of equations that reduce the fractal into that state of singularity. It then gave a long explanation of equations and summarized with,”These equations and steps provide a conceptual framework for reducing the Mandelbrot set towards a singularity through the introduction of an external influence. Adjusting parameters and experimenting with different values will allow for exploring various behaviors and visual effects.” I followed up with would each iteration being drawing towards the singularity appear as a mathematical gravity effect? ChatGPT Yes, the effect of each iteration being drawn towards the external singularity could indeed resemble a mathematical "gravity" effect. In physics, gravity causes objects to be attracted towards a central mass, and similarly, in this modified Mandelbrot set iteration, points outside the set are attracted towards the external singularity. As the iteration progresses, points in the complex plane move towards the external singularity, creating a distortion in the fractal structure around the singularity. This distortion can indeed appear similar to the effect of gravity pulling objects towards a central mass in physical space. The strength of the "gravitational" effect would depend on the parameters ss (the position of the external singularity) and kk (the strength of attraction towards the singularity). A higher value of kk would result in a stronger gravitational effect, pulling points towards the singularity more forcefully. Overall, this analogy provides an intuitive way to understand how the introduction of an external singularity can influence the behavior of points outside the Mandelbrot set, akin to the way gravity influences objects in physical space.
yall ever had a pet that would sit and stare while you did something? That profound cluelessness but still interested? That describes me with any kind of math.
Very nice video. I've been trying to figure out how people actually render those super hi res 3D fractals and really not understanding. So thanks so much for mentioning the term "ray marching." That's just what I was missing!
Amazing video as always! Could you do a video in the future about the haversine function? I feel like there's a bunch of opportunities for interesting visualizations and animations.
The biggest shocker of the whole video is at the end mentioning that you don't know how to create shaders. Your already a force to be reckoned with, once you have total command of fragment shader, every pixel will be devastated
I havent done much with 3D, but Im familiar with shaders~ I would do more 3D but besides PIXIJS I kinda go for the "figure it out myself" approach, so I tend to avoid playing with code that "requires" using stuff like Math.js -- just because I'm super stubborn lol, I'd rather "know how to make it" than to use something someone else already made BUT this is just for the "fun side", in the real world, I'd not be picky like that lol~ Still, this mindset has both helped me and hindered me
Really fun video, and a nice breakdown of the maths. Looking forward to more mandelbulb-related challenges in the future!
I agree! Both of your channels are super inspiring and I'm always excited when I see a new upload. Keep it up!
Thank you, that means a lot!!
It would be fun to see you both team up on this one, you are very talented with shaders and ray marching and that kinda stuff as far as I know
A colab between both of you seems natural for this challenge.
i mean, Collab?
Dude your energy is so infectious. You deserve a Nobel Prize or something. God bless.
this!
it's funny cuz the fractal looks like coronavirus lol
I am always impressed about how you manage to create complex programs without ever defining proper functions, which you clearly dislike :-) Awesome job!
28:00 I was holding my breath, crossing my fingers, and rooting for you. We really really appreciate the hours and hours you spend...to put together these incredible videos. You're the best Dan!
You surely mean 21:26?
Thank you for the kind feedback!
I have no idea about even the littlest thing you've mentioned in this video, but I enjoy your enthusiasm.
This is my favourite channel on youtube. Your enthusiasm is contagious
I remember the video on the Mandelbrot from 6 years ago .. back then I was in high school .. it was around the time when I just discovered the channel and I really loved your content .. my whole family knows about you because I couldn't shut up or stop watching your live streams and videos
I remember also sending the video to my Math teacher and he was truly impressed even though english is not our native language
Man .. I just realised how much you taught me in coding
Thank you 🙏🙏❤️
THIS IS SICK! I've been obsessed with mandelbrot and buddhabrot fractals for YEARS because of your video on the mandelbrot set. I would LOVE to watch a video on ray marching and shaders!!
Yess a coding challenge for raymarching would be legendary
I agree. Please "Fractal god" guide Daniel to render it with shaders. LOL
This video is what brought Processing (and your channel) to my attention. Currently finishing your NOC series and planning to learn p5.js next. Thank you old and future Dan!
Edit: to clarify, I knew of your channel years ago, but I lacked the experience and motivation to watch your videos, and didn't know you had such amazing tutorials!
Welcome aboard!
This was great. Thanks for all your work, Daniel. Such a gift to the world!
Dan, I love to see a new video from you. I am a senior software eng. working in the business for the past 20 years. I love the humanity you bring, along with the self deprecation and humour. I trust Mrs. Gloria Pickle is doing well:) Now to sit down with a cuppa and enjoy this. Thanks again - from Ireland.
Thank you for this lovely and kind comment!!
Oh and yes Gloria is quite happy and enjoying life these days! She says to say woof to you!
You are a legend mate, I have never watched one of your videos without a smile on my face the whole way through!
That was amazing, Dan! "Annihilation" is also a film that shows the beautiful mandelbulb.
Love your content and the way you are teaching the subjects.
One hint to improve your code further (starting 22:50 ): when the edge is set to false you have to add the previous point to the mandelbulb array. What you did was adding then the next point in the line. Because it is a fractal there is a high chance you hit a whole and the next "edge start" will be added but you are missing almost half the points. "Almost" because on one pixel thin "edge switches" you just got it correct
I was looking for this comment. ty !
2022 in March, and your still making videos, even C# developers are watching your videos. Amazing!
Awesome video, I have been into fractals for almost a decade and this was one of the most accessible explanations and implementations of the Mandelbulb I have seen.
The best about the videos is neither the cool outcome nor the educational purpose, but rather seeing how much you love coding. It's so sad how often education fails, just because it seems like the one teaching is not even enjoying it themselves, but this enthusiasm is very infecting :D
I've learnt more from this guy than I have in all my years of school and college, and the best part is how much fun it is. I would be an Einstein if I had a teacher like you.
3D fractals, complex numbers, coordinate transformations, convergence series..... This video has everything! :D
This was awesome from start to finish! Really shows the thought process before jumping into coding and of course all the naunces of jumping back and forth! Good job!
Dan, it's me from 10 years in the future! The video you made looks totally awesome. Don't give up!
Finally waited long for this one dan , thanks for the delivery you chered up a little neighborhood in Bosnia (south europe) much love as always the magic and long train of coding
You make me understand the math part so easily and accompanied all that with your happy attitude it is a work of art. Thank you, sir.
The pure enjoyment is refreshing.
So crazy you came out with this. The last week I've been obsessed with the Mandelbrot set and coding it and was exploring the idea of 3d this is very cool.
Okay that does it. I have no reason in my field to learn these animations but after watching you have so much fun I'm going to learn JS and processing. I have to board the train. Wish me luck!
Welcome aboard!!
@@TheCodingTrain choo choo!
for these sorts of things I would recommend learning GLSL and using shadertoy. much more powerful and not too complicated.
I just found your channel last week, and have just been enjoying these challenges videos. I was having a bad day today but after watching you so enthusiastically solve and explain coding challenge just made me feel a little better. Thanks
Been learning opengl recently and thought about doing a 3d mandelbrot and then found this. Amazing content my man!
Thank you! Please share what you make!
I've been so hooked with the fractal videos from your channel. This is the greatest treat for me. Great work ❤️
This guy explains his process so well, great job
It's great how you make code and maths look easy and pretty fun!
I'm following your first tutirials of Processing and NOC and thanks to them I did a lot of progress.
Thanks Daniel!
Easy, not so much but it is certainly fun
haha, awesome, and fun! I love how the future you interrupts! thanks for sharing
Dude, you are a legend. You are such an inspiration for me and my classes. Congrats!
This guy always surpasses his limits ..next he will create a MandelBulb in 4D wait for it.
Wouldn’t be too hard, he would just have to show a cross section of it at a time. The rest will have to stay as calculations.
or a womandlebulb in 4DD
@@janet.snakehole😂😂
your ability to explain and make this kind of complex things funny are insanely awesome ^^
I have fascination for mandelbulb since it was first rendered. It's the first time I really understand the calculus. So I want to say thanks to you !
this is my new favorite channel on yT.
I love how your future self interrupts/intercepts the video to point out issues with the code and/or explanations given. They way you do this in post production is just really great editing in my opinion. It just shows how much quality your videos have and how great of a teacher you are. Please keep up the great work. Thank you.
Forgot one thing: as a beard guy myself, I gotta say: nice beard. I am jealous. 😂
NO WAY. I've read a thing talking about this before! Also just encountered it in a game I just finished (manifold garden). Never found out how to do it... UNTIL NOW! YEEEEESSSS thank you very much :D
Danke!
Thank you for the support!
i got interested in generative art bc of you years ago and now i'm learning shaders in university
The best coding channel ever!!
This is the most beautiful work of yours I’ve ever seen
These videos are so fun to watch fr
you appear in my feed randomly,,i seriously dont understand any stuff about coding and never tried to learn...but the way you teach its really interesting.....i might give a shot and try to learn coding it looks interesting....thank you
Just stumbled across you channel and am thoroughly enjoying it! I am getting really strong Cliff Stoll vibes from you, and I could listen to him for dayyys.
I made a quaternion raytracer between school and uni (that was around 2002/3) just because fractals fascinated me enough to dig into all that math on my own, which really wasn't easy at that time with only the limited ressources on the web then. Complete with self-shadowing and reflection maps, and a marching-cubes based mesh export for funsies as well to feed it into a "real" raytracer. It even included a fully self-made quaternion formula parser (in assembler, wich I hadn't ever used before, and support for variables to avoid re-parsing every iteration) with all the trig functions and stuff so that I could feed it all kinds of iteration instructions by just writing out a formula in text. Later ported it to an "early GPGPU style" form, under DX9 before any of the actual GPGPU stuff like CUDA and such existed. So just bare pixel shaders.
I think I've never been this proud of any program I made ever since. Man, to have that kind of free time again, sigh!
I never really got deep into the Mandelbulb maths-wise since it "came out" when I was already caught up in studies and work, so I followed this video with great interest and finally, after all these years, understand how it's actually calculated! Thanks!
Edit: Heh, I've just noticed this video came out just one day before my 40th birthday. How fitting :)
The part where you compared the code and the white board was really helpful in understanding it.
Please do it more in other complex algorithms like this
hey, from the future here lol you can take that rendered mandelbulb and save it as an image, and use disco diffusion or stable diffusion to create an image using that image as a mask! this is so amazing, wondering how this could work in python!
The Processing book I read was by Shiffman and half the examples on Processing and p5js site are Shiffman, what a fantastic teacher.
This channel is fantastic.
Not gonna lie I vaguely understand what he's talking about but I love his energy and excitement
A really nice visualization is also how quickly the points spiral away. For that you ramp up the iterations and depending on how many iterations it takes to reach your boundary (should be r>2), you color the vertex differently. For example if your max iterations is 256, then if your tested point spirals away in 5 iterations, then you color it in some way, and if it takes 200 iterations before it grows bigger than 2, you color it another way. Anything that takes more than your limit should be considered part of the set
Just caught up with your older videos and I gotta say your coding challenges have gotten significantly better over the years. Mainly in *how* you do them.
You no longer limit yourself to 10 minutes, you explain what each individual code line does and you're generally much more comprehensible for people who aren't that well-versed in coding.
Way to go Daniel, You're awesome :)
I'm not usually so completely lost in these videos, but apparently Daniel wasn't. He got it to work in the end.
Man, I like your energy.
Can't wait for the shader version! I am actually learning graphics like opengl these days and good stuff on shaders is hard to come by
Imo this visualization is even better than the shaded one! Thanks Dan, awesome video
You are a very nice guy. I love the Mandelbrot idea. Thanks!
Thanks! It has been so interesting! 🤟
The result looks fantastic! What an awesome coding challenge this was :)
I love every video you do, I love the way you teach different projects about coding, love from Mexico :)
Love your videos!
Really great job, Dan. I love your enthusiasm!
Dan still one of the best content internet can offer
Been a java developer for 13 years (recently moved to Node.js though),
Anyway, usually these kind of videos are in Python, which makes it a steep learning curve for me.
I'm so happy to see something that I can actually run myself, and understand to some degree.
Amazing job ! :-)
I'm currently learning Python. What videos are you referring to?? would love to see them
I watched the whole live loved it✨
You said that C gets replaced and then reinserted into z. That is incorrect, and I'm surprised no-one else caught that! The algorithm is that Z(i+1) = Z(i)^2 + c.
That was awesome.
I just wanna add a bit more to the Mandelbrot set. It's story is more closely related to the Julia sets, these are obtained by iterating complex polynomials (z^2+C) and taking all the points that behave chaotically, and the Mandelbrot set consists of all those points for which the corresponding Julia set is in one connected piece. Turns out that checking the condition that you're using guarantees connectedness of the Julia set and therefore allows you to know if that "C" is in the Mandelbrot set.
I really love this channel and everything you do for community. you are the best.
Really impressive tutorial!
Damn this is insane man thank you for this im tripping hard right now i can't wait till i code that myself and look at all those insane fractals
you are awesome, please continue with this valuable job
I LOVE THIS GUY, ENERGY!!
Brilliant teacher
I asked ChatGPT to use the Mandelbrot set fractal and an external singularity to that fractal to create a set of equations that reduce the fractal into that state of singularity. It then gave a long explanation of equations and summarized with,”These equations and steps provide a conceptual framework for reducing the Mandelbrot set towards a singularity through the introduction of an external influence. Adjusting parameters and experimenting with different values will allow for exploring various behaviors and visual effects.”
I followed up with would each iteration being drawing towards the singularity appear as a mathematical gravity effect?
ChatGPT
Yes, the effect of each iteration being drawn towards the external singularity could indeed resemble a mathematical "gravity" effect. In physics, gravity causes objects to be attracted towards a central mass, and similarly, in this modified Mandelbrot set iteration, points outside the set are attracted towards the external singularity.
As the iteration progresses, points in the complex plane move towards the external singularity, creating a distortion in the fractal structure around the singularity. This distortion can indeed appear similar to the effect of gravity pulling objects towards a central mass in physical space.
The strength of the "gravitational" effect would depend on the parameters ss (the position of the external singularity) and kk (the strength of attraction towards the singularity). A higher value of kk would result in a stronger gravitational effect, pulling points towards the singularity more forcefully.
Overall, this analogy provides an intuitive way to understand how the introduction of an external singularity can influence the behavior of points outside the Mandelbrot set, akin to the way gravity influences objects in physical space.
I am in love with this channel
Amazing how fun you are... I want to be like you. Thanks!!!
yall ever had a pet that would sit and stare while you did something? That profound cluelessness but still interested? That describes me with any kind of math.
That was wild, thank you!
12:48 - As a french I completely approve your choice of name...
This channel is so much fun lol
This channel is so awesome!!! This one is a fantastic progression from the original 2d Mandelbrot set video you did!
Cheers! Many thanks
I LOVE YOU
you're awesome keep doing what you do
Very nice video. I've been trying to figure out how people actually render those super hi res 3D fractals and really not understanding. So thanks so much for mentioning the term "ray marching." That's just what I was missing!
Please, please , PLEASE show us how to build and use shaders and do ray marching!!
Amazing video as always! Could you do a video in the future about the haversine function? I feel like there's a bunch of opportunities for interesting visualizations and animations.
oooh, great idea, will take a look!
love your work
Thank you! Very much enjoyed watching this :-)
The biggest shocker of the whole video is at the end mentioning that you don't know how to create shaders. Your already a force to be reckoned with, once you have total command of fragment shader, every pixel will be devastated
That's to reallly cool of like this code!
You are best :D
Thanks for you movies !
Can't wait to clon your code
Bro this is sick
Edit: i loved watching you struggle with the code. Reminds me of myself exept better 🤣
Simply awesome
Thanks for the coding inspiration. Hail Baltimore!
Thank you for your amazing videos! Could you do a video in the future about soft bodies?
This is more cal 3 than I expected
"The square root of -1 is actually something very real" - The source of my aneurysm
I havent done much with 3D, but Im familiar with shaders~ I would do more 3D but besides PIXIJS I kinda go for the "figure it out myself" approach, so I tend to avoid playing with code that "requires" using stuff like Math.js -- just because I'm super stubborn lol, I'd rather "know how to make it" than to use something someone else already made
BUT
this is just for the "fun side", in the real world, I'd not be picky like that lol~ Still, this mindset has both helped me and hindered me
I was about to say that this man has not discovered ChatGPT yet, then I saw that the video was a year ago when chat GPT didn’t exist