Great quote at 13:47 "This is your little mathematical world, and you can do anything you want in it." It's like I'm watching Bob Ross, but with functions.
Its a small thing, but i really appreciate how you alternate between the old and new views when you change something small, it really helps me see the change you have made, as just showing it once really makes it hard for me to tell the difference sometimes
@@InigoQuilez I appreciate the comparison too. however, it is a bit hard to keep track of the graph and the image change at the same time. especially for the vignette effect, mid-green tone pull up, etc. sometimes a left/right split slider animation may be used too
@@rangersmyth Man... His name is Iñigo with Ñ: en.wikipedia.org/wiki/%C3%91 Not Indigo! That is a color! 😂 Anyway, I guess you do not know Spanish, so the mistake is understandable. But if you read the description, you will see the link to shadertoy website, where you can write shaders code, compile it and render images. Of course, you will need to understand how shaders work and all the math underneath to be able to build that image.
My jaw was on the floor for half of this. I almost can't believe it's possible to render this much detail in real time. You have no idea how inspiring this is!
Talking about Inigo, my jaw is on the floor because I can't belive it's possible for someone to know how to apply THIS MUCH of math with such clarity. I guess it's the most impressive technical feat I've ever seen!!
It is realtime, yes. Just click the Shadertoy link in the description of the video, it will run on any browser and relatively up to date computer. It could be much faster, the ode is optimized for being mathematical, no fast. But still it should ran at 30 fps at least in a gaming PC.
@@InigoQuilez I'm excited to try this program; I have been looking for something just like this for a while. Until then, I'm going to need a lot more mathematical experience! 😅
The quality in this videos is amazing, I love how he uses 3d animations to explain all the equations. it makes it so easy to understand what each thing is doing.
@@daonlyowner6631 No. He's just taking reverse direction from sunlight with average terrain color and an ad hoc multiplier. On average, that's going to be in the ballpark. Though, the multiplier needs to be hand-picked for sun elevation and terrain shape, but since this is done for a set piece, that works!
I find it fascinating how detailed the perception of some people is. I was already convinced of the scene but hey, let's add some little yellow here and another bump there... Very impressive! 👍🏻
I remember bumping into Inigo literal decades ago when first getting into computer graphics. Literally 90% of everything I know in that area comes from his website. He's like the Knuth of CG, reading through his articles feels like perusing a sacred text, equal parts art and math, all of it genius. Very happy to see him here after all those years. Makes me itch to play in ShaderToy.
Same with me. I saw his demo "Elevated" back then in 200 9live at the Breakpoint demo party and I was blown away. Little did I know that the creator of this masterpiece would also become a master of teaching others and sharing his knowledge.
@@slickytail Shadertoy's preview window is 800x450 at which it runs around 140 FPS on my PC. The drop is quite significant at higher resolutions however, on my 1440p monitor at full-screen it runs below what I consider smooth, I'd say it's about 30-40 FPS, not sure how to get the exact number there. But it's still certainly way more than 3 FPS :)
@@AdriansNetlis On my laptop it runs at 3 fps in fullscreen (1080p). Let's not even talk about phones! Just pointing out that the majority of users are not using hardware that will run this in real time.
@@tornado100able Absolutely, mostly with noise functions seeded on the basis of the chunk to generate. If you are curious, you can check this out: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Nj8gt_92c-M.html
This is fantastic, not only paint but created the world with mathematics alone and no real source feed into it. The maths involved is advanced but not too harsh, which is an eye-opener for people to learn math and programming. You are awesome.
I barely know anything about 3d graphics but still watched it till the end....What I liked is the underlying maths, which i understood to the some degree. can't thank you enough for sharing your knowledge...
Now I understand why are we made to study these topics in class 11 and 12 in India and what's its application in real life. Also got to know today that this world is literally mathematically built.Thanx to you.This indeed is beautiful to know the details of our universe.
As someone aspiring to work at Pixar once I graduate, and as someone who loves math, this video was an absolute gem. It was delightfully composed and the end result was breathtaking. Thank you for making this for all of us to see. I have no doubt it was a lot of work.
Very nice tutorial! You are someone who has been spreading the word about ray-marching for many years - thanks to that I found out about this great technique (from your website ~7years ago) - thank you very much!
Sometimes RU-vid's algorithm hits you out of nowhere with an absolute gem of a video. This was amazing! Thank you for your teaching and for making the code available. I will study it and use it as a basis for my own mathematical paintings! In fact, I always loved constructing the functions that I needed out of small, fundamental pieces. If you ever want to do the same thing with sound, Csound is a very old tool to do just that. (But there are probably better tools nowadays?)
This is by far one of my favorite math videos. I did not understand all of the math but this was still so interesting. I never knew math could be used for this
I didn't know this was even possible. I didn't understand a thing and I am very impressed with everything And this is clearly the most magnificent mathematical painting I have ever seen! Good job!
This has to be one of the most beautiful videos I have ever seen on the internet. You sir have made a MASTERPIECE of a video. I cannot describe how engaged I was through the whole thing. My jaw was always on the floor
Holy wow! I new math was powerful, and in the back of my mind I know this is how my drawing programs work under the hood... but to see this scene built with ONLY math equations sort of kind of blew my mind... This was really cool.
I once wrote a high-school paper about approximating the surface areas of hills using piecewise functions (the functions were only linear however, I could not deal with more than that back then), it's really awesome to see someone take the concept to such a degree, incredible video!
Absolutely beautiful , and was engaging for the entirety of the 40 minutes. Thank you for sharing this and making videos of this calibre free to watch.
Stunning. I have never seen mathematics applied in such a beautiful and captivating way. You are the multivariable calculus da Vinci. Everything in this video was presented in a precise and masterful way. I would LOVE if my students could make something like this for a final class project. Thank you for sharing your work and for all the surely grueling hours it took to produce this excellent video.
It felt great to need out for over half an hour and see mathematics I use everyday be applied in creative ways. It also showcases just how powerful linear algebra and calculus are when used together.
I am not into math or anything I didn't even search this but it got recommended and the title was too catchy. would be fun if they taught us such stuff at school. this looks so fun! it's beautiful
I am almost lost for words. 😶 It’s brilliant and I understood bits of it but the rest just short-circuited my brain 🤯 I expect I will have to watch this over and over. Thanks for sharing.
You’re back! Look how far even the master of shaders has come by working with Pixar. In this video I feel you’ve not just done great mathematics teaching, but deeply connected with artistic expression. I was waiting for this one! Congratulations on finishing.
This presentation is absolutely wonderful, I've been having some trouble getting the general math concepts behind some of the code I see out there, and this helps a ton. also holy crap that 3/4/5 matrix trick is beautiful
First I was surprised that 40 minutes had passed. Then I was surprised that I had watched the whole video again. Thank you so much for this. Late to the party, but this video needs all the attention it can get.
This is one of the first videos I've ever seen like this. I'm a computer science student so I've seen people use really complex algorithms to achieve realism, but I love the simplicity of this. Hope to see more videos like this because I find them super interesting.
I'm only 2:30 into the video and my mind has already expanded 100x Thank you so much Inigo both for your amazing art and your amazing love of sharing knowledge!
I love this video so much. It is really helping me understand some fundamental low level concepts much better but also conveys the design process so well without ever getting stuck on details.
I always wondered about this piece, but when I looked at the code, I was just baffled by everything going on there. I'm studying Electrical Engineering, but when I'm bored laying out circuit boards this type of art is a fantastic way to do something different and at the same time learn something new :)
I am actually an electrical engineer too (I did my Masters, I mean). This Paintimg with Maths stuff was my way to have a break from semiconductors, Maxwell and Shannon :)
@@InigoQuilez I also want to thank you very much too, because I as well am approaching the end of my Master's Thesis in Electrical Engineering & Information Technology, and your incredible work with shaders inspired me for my thesis topic. It takes place in the medical domain, and is about simulation of a specific microscope. I create artificial images from blood cells modelled with SDFs, by doing sphere marching with some tweaks for lenses, depth of field etc.. This yields training data for machine learning, which in turn can then hopefully reason better about patient's blood conditions than it does currently. Also your video is absolutely incredible! I cannot imagine how much work that must have been
I'm totally in love with your art and explanations. It is trully inspiring to see how far we can go in generating art simply by tweaking numbers and formulas, even if we don't get the science behind it. Big thanks for your work IQ
This was honestly the most useful and insightful video I've watched in a very very long time! I love applying the math I've learned from my undergrad to something creative, so thank you!! Also, someone else in the comments mentioned "It's like I'm watching Bob Ross, but with functions" - I have to second this statement. Well, done, sir.
Holy moley, I have been messing around with 2d math art for 4 years as a high school student and just started on a homegrown orthographic projection. Looking at this is like stepping into the 1000+ years future of what i was playing around with. its surreal. It's crazy. its mind-breaking. so fucking cool. You've just shattered my reality.
@@marcianoforst6311 I'm a high school math teacher and I promise you that although most of the video went over my head, it was because of the speed and my wonderment and not the complexity of the maths. Everything done in this video is within the grasp of a good high school math student had they the interest and time.
The combination of the terrain normals with the tree normals is brilliant and really shows the shape of the terrain and makes the image look so much clearer. I love these videos!
This video prove that you have master maths. This is so awesome. I understood quite few things cause of my engineerings maths class but still so much more in this video. Good job man.
