Painting a Landscape with Maths

[@matthewkaemmerer7569]

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.

[@DavoGalavotti]

I was thinking about Bob Ross as well, when Iñigo said: “happy little clouds” 🥹

[@g-pr]

I‘m quite sure this phrases are a tribute to Bob. A „Hommage“ in German.

[@millercentretheatre]

And "happy little trees"!

[@g-pr]

@@millercentretheatre For sure. Also noticed :)

[@Smittel]

"Happy accidents" is also something i at least associate with BR but im not entirely sure

[@randyprime]

this is fucking beautiful

[@marsl8603]

Honestly, I'm not suprised to see you here.

[@user-pn4dp4br7n]

Hopefully he doesn't try to recreate his game using only maths

[@wellox8856]

oi

[@Cayman_Clubsport]

Language

[@timothymakesgames]

Fancy seeing you here mate

[@amyshaw893]

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]

Noted. I'll do more of that and better next time

[@ethancheung1676]

@@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

[@InigoQuilez]

Yes, I totally agree, I'll try the slider idea next time.

[@rangersmyth]

@@InigoQuilez Hey Indigo, outstanding work! Wondering what program are you using? I would love to learn how to do this!

[@nephew_tom]

​@@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.

[@fudan1]

Just came from a class and my professor showed us one of your videos, and he said that you're basically his idol

[@RobattoJ]

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!

[@halian.vilela]

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!!

[@agfd5659]

I thought this was rendered offline

[@Lumegrin]

@@agfd5659 Did he say it wasn't?

[@InigoQuilez]

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.

[@Lumegrin]

@@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! 😅

[@kanoest]

This shows the beauty of mathematics that I never knew existed. The concepts and executions are peak maths understanding on high level

[@sam_phys-yz7fr]

Its extremely nice but just basic (but very clever use of) functions. Not high level math.

[@konstantinkh]

Me: "Bounce light is going to be a nightmare with this terrain." Inigo the Wizard: "Super easy, barely an inconvenience."

[@konstantinkh]

@DaOnly Owner 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!

[@dsp4392]

Bouncing light is TIGHT!

[@dmitriytuchashvili8594]

didn't expect Pitch Meeting reference here

[@matsv201]

@@konstantinkh UE5 does a simular trick when it have a very low res map of every object to calculate bounce light of. Its very convincing and pretty much impossible to spot.

[@konstantinkh]

@@matsv201 Technically, UE5 can do lights however you want. So can UE4. I haven't looked too much at what comes out of the box in 5 in terms of lighting, but typically the way you set this up still involves baking some sort of a map. State of the art, if you aren't doing rays, is to have light probes for local GI and then have a global map as a final fallback for either low LoD or missing probes. Typically, each probe + global will be stored as spherical harmonics, but that's matter of implementation. You can bake it down to single vector + intensity for really low res estimate, so equivalent of having a directional light. Bottom line is that it involves baking some sort of data from the scene into effective lights. Having the developer do the "baking" in their head is very retro. Reminds me of the days when environment artists would place fake light all over the scene to simulate GI. Very 2010. (That's like a century in graphics years.) I just wasn't expecting that in a modern SDF marching rays demo.

[@diegolg1189]

Just beautiful.

[@g43s]

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.

[@gordonfogwill4885]

40:21 The clouds shifting and the shadows following was absolutely delightful to watch, and made it seem like a time lapse. Great video! :)

[@qTnD42hR]

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.

[@ruedigerraab4089]

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.

[@HyperMario64]

This is a masterclass. And completely deterministic, this could run in real-time. Oh wait, it does!

[@slickytail]

If by real-time you mean 3 FPS, sure.

[@AdriansNetlis]

@@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 :)

[@slickytail]

@@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]

Well, Minecraft generate "square" words following some kind of mathematical formulas i guess

[@HyperMario64]

​@@tornado100able Absolutely, mostly with noise functions seeded on the basis of the chunk to generate. If you are curious, you can check this out: kzbin.info/www/bejne/hJubmKeVbpeWY68

[@wargreymon2024]

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.

[@w花b]

True, I was surprised to know all of these functions that I've seen in high school, that was surprise but a welcome one.

[@parsuli.]

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.

[@davecgriffith]

The art here is actually this video. Fascinating subject and wonderfully presented. Thank you for this!

[@MatijaHan]

Thanks!

[@InigoQuilez]

oh wow, so generous, thanks a lot!

[@euphonic3466]

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.

[@ankur67678]

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...

[@konya8248]

Man.. this is impressive it's like he's explaining how people back then are doing it, but with the current beauty of today's engines.

[@Lucas72928]

You can really tell the amount of work that goes into making one of these videos. Great work!

[@wiredlifter]

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

[@emp9083]

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.

[@angeltodorov4577]

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

[@_shroob770]

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!

[@chrisxd146]

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.

[@tizilogic]

You are definitely the Bob Ross of mathematical art!!

[@firefly618]

Sometimes KZbin'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?)

[@MathIsGreatFun]

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.

[@gbkEmilgbk]

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!

[@iestynne]

This is a great educational legacy you are building here, to inspire the next generation of graphics programmers. Bravo!

[@TriggerlyDev]

Me not understanding 90% of the video but enjoying the visuals

[@DaveChurchill]

As a computer science professor, these videos always blow me away. I wish I could create lectures of this quality!

[@christelleaugustin1695]

Just play this video

[@claytonleonardcook]

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.

[@bytesandbikes]

appreciate the Bob Ross references!

[@krpnz]

Thank you Inigo for this video, and for all of the detailed articles & demos on your website for many years.

[@JonathanJumper]

This a whole other level man, max respects I'm an computer engineer myself, but this is pure math, and an art the way its presented

[@HiHi-iu8gf]

waow the noise for the trees works way better than i'd have thought

[@niklas2430]

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.

[@christelleaugustin1695]

Don't you mean "high-level"? If you talk about "without getting stuck on details"

[@PolyRocketMatt]

I think it is beautiful how something many people don't like (mostly because they miss the engagement like this) can result in one of the most complex yet simplistic, elegant yet basic things there are. Thank you for providing these wonderful videos!

[@swampflux]

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.

[@hfs-lk5ip]

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.

[@nurse_plissken8433]

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

[@redlaserbm_phd]

Okay, this is cool! Didn't think much of the polynomial surface till you started adding scaled and rotated copies on top, that was brilliant!

[@BoyceBailey]

It's just a joy to watch this. It like watching the grown ups do something you're amazed by but when you're an adult.

[@StevenHokins]

❤

[@lunafoxfire]

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!

[@nobodynoone2500]

Brilliant. Maybe the best explination of where you can use math creatively I have seen in years.

[@plazmaguy13yago9]

Even tough i can barely understand some of the steps you do i find this incredible!

[@maymayman0]

You truly have one of my favorite channels on KZbin, and I watch way too much KZbin.... thank you for everything you do

[@somethingthatpops]

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!

[@nameno7032]

you teach code, math, and art at the same time, what a beautiful combination Hope you the best, and keep making these

[@Conobipe]

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

[@gamesvrtech6666]

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! 👍🏻

[@icaroamorim3123]

Wow I can't describe how amazing this is

[@TannerCh]

This is one of the most incredible things I've ever seen.

[@Invalid571]

This video is sooo beautiful, I watched it in it's entirety twice!

[@vlahovivan]

This is the best video I have ever seen on KZbin

[@ハェフィシェフ]

Your animations, for instance of the normals at 26:13 are absolutely amazing

[@Ontropy]

The animations are top notch, makes it really really easy to understand the functions. Really good explanations as well. Thank you very much. Thanks for attaching the code too.

[@isaackay5887]

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.

[@lucianojadur]

One of those few videos in this whole site that everybody could describe as "perfect". Genio total.

[@Anonuser11131]

Keep making these videos man, you have found an audience.

[@alexmarunowski6442]

I watched this entire video with my mouth agape. Purely magical to watch.

[@lightninghell4]

Combining physics, math, and computer graphics to create a staggeringly beautiful painting. Amazing video man.

[@benwesch1405]

This is incredible. Thanks for sharing so much knowledge in such a beautiful way!

[@thomaswatts6517]

this is the coolest thing I've ever seen, the fractal surface sum gadget is sick!!!

[@snippletrap]

Beautiful. I could watch the clouds roll over that landscape all day.

[@CarstenMeyer]

Another free lesson from the master himself! Great as always!

[@male20yearsold]

everyone who's making a digital art is actually making "mathematically" art. The digital brushes, colours, canvas, etc. it is all math. what we saw in this video is very mathematically from the very base, real definition of "from a scratch" with no instant tools like digital brushes or etc. Appreciate it Inigo Quilez! Very Amazing and inspiring.

[@kayaba_atributtion2156]

Wow this was beautiful to watch! You should make a Ted talk

[@RhogerAnacleto]

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!

[@Demoscene0x0801]

If my mathematics teacher had told me 30 years ago what incredible things you can create with mathematics, I would have slept less in class. 🥺

[@christelleaugustin1695]

Exactly

[@pinklady7184]

I am 3D artist and animator, and I am learning mathematics for 3D realism plus physical simulations?

[@marcianoforst6311]

This is not simple math like what you learned in school

[@poutouellet]

@@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.

[@marcianoforst6311]

@@poutouellet Calc 3 in high school?

[@arindamn4880]

This is the I'd absolutely love to learn. Great video sir!🤩

[@rusticagenerica]

I love this concept

[@probablynot8154]

yes!! these are some of my most favourite videos on youtube.

[@3kcozadurnylol]

I'm absolutely impressed by your work. It is the first video that I saw, but surely not the last one. The harmony between beauty and maths is like visiting an art gallery, theatre and dancing at once. Almost spiritual experience :D Great work!

[@vladshcherbakov3112]

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 :)

[@InigoQuilez]

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 :)

[@SimonSchumann]

@@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

[@Mukesh_Rana._]

I am also a student of electrical engineering 👍

[@Emboar565]

Thank you for this video. I am a 1st maths student and I enjoyed every single second of the video. I loved all the work and quality on this video from the way to explain it to all the animations and equations. The result is espectacular and beutiful.

[@DenisIsidoro]

I never comment in videos, but I had to this time. This video is fantastic in so many ways: presentation, teaching, Math elegance, etc. Excellent work!

[@RGBguy]

You are a genius! An inspiration! Thanks for the content Inigo. Just love it!

[@lovelybunny9190]

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

[@brycepoteat1928]

I would watch a hundred of these videos that are a mix of art, math, and tranquility. Absolutely beautiful!

[@Ra11y]

This was absolutely incredible!

[@rysea9855]

Wow, this is an amazing video. It's a very fun video to watch, and even though I probably won't try making this myself because I know nothing about programming, I still learned a lot. First 30+ minute video in a long time that I've been able to keep my attention to the whole way through, and that's saying something. Really well made

[@Philoreason]

This is the best video I've seen explaining how landscape generation and rendering is done! good job! Thx!

[@lucabilotta]

Inigo your work is absolute stunning (I've seen among many, your "Elevated" 4kb winner of democomp) From an Italian fan, you are The Leonardo Da Vinci of mathematical painting and procedural gfx!

[@randompast]

You are a wizard, thank you for sharing your wisdom with us. I am inspired to play with these techniques.

[@christelleaugustin1695]

i understand nothing but if i were smart i would understand it directly because of your visual clear explanations!

[@AzharulIslam1]

I can't believe it. Oh my GOD!!! It's awesome.

[@DJR3H]

If I ever have 1 year of time to spare - I'll try to understand all the math I just observed. Beautiful

[@InigoQuilez]

It is true that mastering anything does take time

[@benedictsth]

So much love to detail!

[@123lex123]

Honestly, this almost made me cry. The fact that this is all just math is so extremely beautiful!! I'm a computer science student and secretly in love with math. I think you just showed me a door I was looking for! Thank you so much!!

[@imnemo2327]

could you tell which branch of mathematics he is talking about in video.I didn't understood much!!!

[@lakshyarajsinghrathore1902]

@@imnemo2327 mainly algebra and calculus

[@trevorleake2010]

I've been a fan of ShaderToy for so long. Thank you Inigo!

[@harrybmichell]

What an incredible video! I'm taking a computer graphics class and this is just blowing my mind

[@lumarans30]

That's amazing! Great work!

[@oliverrevis4190]

This looks remarkably similar to the Blue Mountains in Australia. The Grose valley in particular

[@merimbungur7168]

This is the best thing youtube has recommended to me in years. I am simply amazed how well you apply mathematical concepts to get what you want. I made sure to subscribe and go down the rabbithole of your content

[@OkiSuwen]

"So do you use oil paint? Pencils? What do you use?" "NUMBERS."

[@yah3136]

Awesome, both the explanations and the result. Mind blowing

[@voidbreak4756]

As a Desmos user, this has inspired me so much! I hope to try something like this when I'm older! I need to wait 5 years for university though, argh!

[@iwikal]

No you don't! There's tons of info online about linear algebra, programming and computer graphics! I recommend 3blue1brown on KZbin for the linear algebra stuff. As for the programming part, you'll have most luck searching for guides and web books about your particular programming language of choice. Mozilla Developer Network has a nice beginner's guide to WebGL for graphics in the browser, for which you will also need to know some basic JavaScript, but the internet is brimming with educational content about JavaScript. You'll find it if you look for it. There's other avenues though: you can learn Blender, or a game engine like Unity, Godot etc, or you can learn some other programming language and a native graphics framework. Just pick something that piques your interest and get started!

[@iwikal]

To back my claims up: I'm 25 and a uni freshman, but I've been doing computer graphics as a hobby since way, way before university. I'm mostly going to uni for my interest in deeper maths, the kind of maths you will never need as a programmer or technical artist.

[@voidbreak4756]

@@iwikal Oops! It seems like I've worded my comment wrong. I actually meant that I would try it, but I still have to wait 5 years for university. I don't know why I put the university part in lol, they don't matter. Anyways, some of people on the Desmos server and I are working on some code that would make Desmos work sort of like Shadertoy. Thanks for the inspiration, though!

[@iwikal]

@@voidbreak4756 have you tried shadertoy? I'm pretty sure you could make this exact scene in shadertoy. Just translate the expression to glsl and slap on a projection matrix! Super easy in theory haha, it'll just take a while. The framerate might not end up being the best though.

[@MScienceCat2851]

@@iwikal Snice im not good at math, what turials are best and what math was used in this video, its advanced

[@vildauget]

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.