Coding Adventure: Boids
ฝัง
- เผยแพร่เมื่อ 31 พ.ค. 2024
- Trying to create some flocking behaviour, and getting a little distracted by spirals along the way...
Links and Resources:
Project source: github.com/SebLague/Boids/tre...
Boids paper: www.cs.toronto.edu/~dt/siggrap...
Points on a sphere: stackoverflow.com/a/44164075
Fish shader: github.com/albertomelladoc/Fi... and www.bitshiftprogrammer.com/20...
If you'd like to support the creation of more programming videos, I'd greatly appreciate your support on patreon:
/ sebastianlague
Chapters:
0:00 Intro
0:26 The three rules of being a boid
1:44 Obstacle avoidance
3:03 Getting sidetracked by spirals
6:12 Back to obstacle avoidance
6:55 Obstacle course and optimization
7:47 Swimming with the fishies
Music:
"Beauty Flow" Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 4.0 License
creativecommons.org/licenses/b...
When you combined the boids and underwater marching cube projects. My mind got blown.
all that's left now is to put this water/fish system into the eco system he did.
I said out loud "Thats so fucking cool!"
Then you definitely will like ABZU game.
@@Sparrow420 I think he could make CoD Ghosts now, he has fish ai!
I would buy that no cap.
Ok, now this series is really turning into Subnautica development
This goes faster though
Making the game is the easy part. The hard part is the other 99%.
I really really like this comment
@@tomohawk5411 i like it too
I truly apreciate this picture (your profile image) very, very, very much.
"Me and the Boids at 2AM" was literally the first thing that popped into my head.
Jokes aside, it looks fantastic!
Or maybe you copied
@@pikachu-jf2oh or maybe this is the original
@@grownman9984 or maybe this is the simulation
Actually watching this at 2am
@@RASD87 2,05
Would that be called "Obstacle Aboidance"?
I'll let myself out.
@Haph try and aboid making such dad jokes in the future.
@@benardnguyo6817 Ha, his jokes are so bad, his mind must be a boid.
boids will be boids...
Don't let the door hit you on the way out.
H
Me and the Boids, watching a new great Coding Adventure
lmao
Cracking open a cold one with the boids
You watch that new amazon prime series, “The Boids”?
UGE Those Twitch ads are so annoying
Rafale25 I binged it all it’s a good show. Flixtor.to is a website like Netflix but has EVERYTHING YOU COULD EVER WANT. I bought vip for rlly cheap.
This sphere raycast system using fibonacci sequence blew my mind, this is really awesome and very well explained ! Great series, please continue like this !
Happy you enjoyed it :D
@@SebastianLague Chapeau for your great explanations. I don't know why I feel that those coding explorations are actually really great dev logs and we may get a kick ass game after a while! Keep up the excellent work. I'm learning a ton from you and you inspire me to learn even more on my own.
Yeah i’d love a more elaborate video on that!
@@SebastianLague I saw something similar a while back, th-cam.com/video/rwV_dAlWWnw/w-d-xo.html video titled "N Equidistant Points on a Sphere"
Should have just used spherical coords-choose angle1, angle2
"I don't need math, i want to make games" :D
\*creates entire physics model\*
@Holy Spiritual Practices Good to know. Imma keep it the way it is though, so people understand your comment.
Tbf I make games and I'm completely lost with the above.
@Holy Spiritual Practices It's not commented out tho. It's two nested opened multi-line comments... so this is not even the comments' final form!
@@TheAero1221 backslashes? guess you are a diehard windows fan lmao. :P
I love how you can put a few simple instructions into a computer and get something complex in return.
"simple instructions"
That's emergence for ya
Emergent behaviour is almost always amazing
Try doing it yourself. IT'S NOT SIMPLE.
@@basicallybrand Specially if you remove some degrees of abstraction. The generation of points (the first part of the video) is rather simple in C. Try making that in assembly. Or take a look at how the video card interprets them. Making something complex from the most simplified instructions is the bloody purpose of computers.
That's so cool! Math and nature is crazy man, damn
Thanks Dani! :) Yeah that stuff boggles the mind
Dani?
Martino Ericsson ik
Hi Dani you got me into coding and I’ve watched nothing but coding for days. :)
WOAH IT'S THE REAL DANIIIIIIIIIIIIIIIIIIIIIIIIIIII
When you realize "boid" is just "bird" being spoken in a new jersey accent
Spring is sprung, the grass is ris.
I wonder where the boidies is?
The boids are on the wing.
Now isn’t that absoid?
I always tort the wing was on the boid!
Jersey birds are just pidgeons with bad attitudes.
You catch on quick.
Eggs?
What about the eggs?
Plastic!
Yes, plastic, in whatever color you can think it!
Craig Reynolds said the term is a contraction of birdoid... boid!
Let the boidies hit the floor!
i could do this in my sleep
i learned ' print("Hello world") ' yesterday so im pretty much a expert
stop flexing on everyone 😭
Ikr made a calculator... pretty much a god now
@@BeardedButter I made a calculator in python that makes sence at the time.
I remade it after I mastered python and it wont work
@@nathann1445 lol
bro how
3:25 I can't get over how you drew this phi so beautifully
This is so cool, do you have plan on brining the boids, worlds and ecosystem together to create a little planet ? Thanks for your work
Maybe add even "land boids)
@@gustavowadaslopes2479 Or rabbits and foxes.
@@FlyingDominion They felt kinda stiffy compared to the boids.
I guess if they get slightly deeper behaviors (camouflage, hiding and maybe tracking/smelling.
@@gustavowadaslopes2479 I would love to see the ecosystem expanded on with more realistic behaviors.
@@memeymeemerson5426 Yeah.
I think seeing some sort of "ecosystem" for a game or simulation game being done animal by animal followed not only by evolution but also by new behaviors implemented and new environments.
It would be like seeing a documentary about evolution on earth, but being able to use completely new environments and systems, while keeping everything considerably simple and engaging.
The auto-generated subtitles at 0:05: "I'd like to play around with some boys"
Well ok then
Just saw this - legend :D
Those are girls
oh shit
I love that the fish move out of the way when you get close to them
You should add an enemy (e.g. shark?) like the rabbits and the foxes
Xaracen for sure but if that would it would be mad
@@xaracen7207 Not so sure about that. While it would eat quite a bit of performance, it should be doable on a decent computer if optimized accordingly. He does most things on the GPU since he learned about compute shaders, however there are also ways to utilize the CPU efficiently. The rather newly introduced Burst Jobs in Unity for example. Not only are they a comparably easy (and completely safe) approach at multithreading, the speedups are also pretty ridiculous. We are talking in the regions of factor 10-50x speedup. Properly utilizing the CPU with burst jobs, plus the GPU with compute shaders, would definitely allow for a pretty darn complex simulation to run smoothly. How complex or how smooth exactly will depend on the hardware, as always.
@@Yamyatos Really it would not be that intensive. The eroded terrain would be baked. The bot code could be done with collision spheres triggering the code.
Im not an expert in programming but i think that that would be easy... you just need to program the sharks to avoid obstacles and catch the nearest boid (group of things) and program it to do at random time
Add shark hunger systems
I like how you explain the algorithm in every video so enyone can implement it in any language (dx, opengl, vulkan ...) or engine.
5:32 - God DAMN
When that distribution got corrected, I FELT that!
You're like the 3blue1brown of coding.
You explain everything in a manner that can be understood very easily, and I like that.
3blue1brown does math, while you do code.
Bob Ross + 3B1B + Code
Edit: Although 3B1B is kind of Bob Ross + Math, and (good) code includes math anyway, so I guess we can remove that overlap.
@@LabGecko I feel like coding train is more like Bob Ross
I just noticed that your editing is absolutely masterclass. The effort put in to have what you say sink in to what we see is commendable. You're the best Sebastian Lague.
Fun fact: the original Half-Life game includes a boids implementation. It can be seen in a scripted sequence as flying critters in Xen.
If you search TH-cam for "half-life boids" the first video shows this.
Yeah but they went with the "leader" approach, which is not as realistic. Still, great stuff to watch
This is one of your best videos! The step-by-step visualizations as you implement each part of the code is seriously next level, and makes these really complex ideas far more palatable.
Can't give enough praise for your work on this format. It's seriously fantastic. Keep up the awesome work!
Also didn't realize you had a Patreon. Please give it a shout out in your next video so people know they can support you. Im signing up right now.
Thanks so much :)
When you make cool lookin stuff like this, make the showcase at the end longer please. The serene visuals and music were kickin, wish i could have watched that for a minute or 3.
I wanted more of that end also, the stuff he makes is amazing.
COD: *Revolutionary Fish AI!*
...
Sebastian Lague: *Three lines of code*
Came to the comments looking for this... To make it look even more real just add a huge repulsive force whenever something big happens in the game like shooting or so...
I love these videos, I learn so much neat stuff from them! This is my favourite coding series, I can't wait to see what's next.
Is nobody gonna talk about how mesmerizing it is. It looks like a school of fish.
It would be interesting to see how the behavior changed if you added a predator with its own set of instructions and had the boids add in some sort of "avoid getting eaten" rule to their existing rules.
I may be a 7th grader but that won't stop me from trying to understand These equasions.
This video is FANTASTIC .
Thank you so much for what you do!
LOVE your work.
I love watching these videos as it greatly inspires me to continue working on my projects and to get coding and learning more. Keep up the incredible work!
Outstanding work. Your humility makes trying this myself infinitely less intimidating. Thanks for taking the time to make these videos Sebastian.
I read somewhere that each bird only needs to be aware of 7 nearest neighbours. They probably estimate to remove the blind spot, too.
How do you even come up with these things? Like, you start with a known example of individuals moving together in groups(boids), and end up with something that can be used as a 3D pathfinding solution.
I did a Game Development study in Amsterdam and we covered most of these things (apart from the ecosystem). Next thing would be a particle-based fluid simulation. If you have an interest in this kind of topic you quickly find these fun challenges. He does go really in-depth into the topic which makes it really cool!
@@programereniscoolwhere to find these fun challenges
@@tushargupta764 Unfortunately, school is a big factor. Teachers really think their courses through. You can look for it yourself. If you see something interesting try to make it yourself. I personally really like optimizing, rendering and voxels. So now I am building my own game framework in C using Vulkan and Octrees. If I learn something new I apply it to this playground. Now you got to decide for yourself and create time to do some fun things that keep you motivated. Why did you get into programming in the first place? What inspired you?
@@programereniscool What if someone wants to learn it all but can't go to programming school?
@@kaksspl You can always learn by just doing. The hard part is figuring out what to learn next and to stay updated. Personally, if you are really serious about it you can check out the Open Source Computer Science Degree (github.com/ForrestKnight/open-source-cs ). This page has a lot of different courses that you can follow or you can use it to find out what courses you should know more about. Hope this helps a little!
None of the senior thesis presentations I saw (before lockdown) were as interesting or as well done as this... and it looks like you make these videos super regularly. Subbed!
I really *REALLY* like the way you present what's going on in these videos (I'm not a programmer, and my math skills absolutely suck - but even I'm able to follow along with your logic progression).
This is awesome!
As a person who makes their living writing software professionally, I feel the need to tell you that programming is more about solving logic puzzles than about having solid math skills.
The underwater scene you made at the end was so amazing! Even though it was just a simple and not very detailed map and some simple fish it really did feel like you were underwater! Amazing!
best, do you want to make an erosion video in voxel space ?? would be super cool
I may be off, but that is what his underwater scene was all about. Maybe your asking for a different technique.
@@micaiahstevens8840 As I recall the terrain in the underwater scene just comes from using marching cubes to render a surface on some 3d perlin noise. Erosion is a technique for modifying terrain using simulated weathering processes to generate features that you don't see in pure noise-derived terrain (like sharp mountain ridges and valleys)
Awesome thanks PKMartin. He did make an erosion video, but with meshes not voxels as well. NOT say I don't want more videos from Lague hehe!
And the natural selection simulation built into the fish boids.
I'm really happy that you're back, can't wait to watch this :)
Wow, you have no idea how seeing these two projects together felt great. I dont know if you had that in mind from the beggining of this project, but it really adds up to the channel. Please continue building things that go along with those two.
This is definitely the coolest mix of art and technology around. I don't think I would have thought to put those two projects together. It's obvious once you've done it, though I think you deserve credit for that apart from the whole.
aaaaand 3 lines of code later it looks like magic, again. Why can't I code like that?!?!!?
I think it is not about the code itself, but what he was coding. His starting point was a paper. His coding is beautiful, but the idea of coding a studied behavior is even better.
Because if your code is well written in the first place, adding new features can be just as simple as adding couple of lines
NOT to discredit Sebastian amazing work, but some of this is well documented code, he is adding his own flare for SURE. That's why its simple yet elegant its like taking 10 sebastians and making amazing code. He listed out some of their names. Including the original author of the Boids code. Almost like the author of Cellular life. IE the Game of Life, by Conway I think.
probably too much grovelling and not enough study
Sure, I get all of your comments. I'm a programmer myself, and we regularly code from papers (specially geometry stuff). But still, the fact that you can put < 50 LOC and get schools of fish freaking floating around your marching cubes terrain and avoiding your submarine... well, that's something else.
Amazing video Sebastian. Flocking behavior is really an interesting subject. This leads to an Emergent behavior... How an object can react exclusively to its neighbor behavior. Awesome as always!
It's so fascinating to see little tiny cones swimming in air.
Creating and evenly distributed set of points inside a disk is called phyllotaxis. Here is a javascript function that returns a function that gives the coordinates of the ith point in a phyllotaxis, ensuring that each point is separated from its neighbors by a distance d:
function phyllotaxis(d) {
var theta = Math.PI * (3 - Math.sqrt(5));
return function(i) {
var r = d * Math.sqrt(i), a = theta * i;
return [
r * Math.cos(a),
r * Math.sin(a)
];
};
}
// enjoy !
the underwater exploration at the end looked super relaxing, i'd probably buy it if you added a few more features and sold it for like $10
Looks like a good candidate for VR.
Get Subnautica - it's awesome.
Something like this? media.giphy.com/media/2xEAuD1mqqjk7ul1Pp/giphy.gif
Beyond Blue is an underwater exploration game releasing this year on PC, Xbox1, PS4, and on Apple Arcade, if all goes well :)
Come follow us on twitter.com/BeyondBlueGame
(I can't speak to the actual price, probably a bit more than $10 but less than full priced)
@@geoffcunningham6823 Yeah, but the simple graphics are really refreshing.
Damm your coding skills are amazing! My favorite unity related channel on TH-cam 👏
This is one my favorite coding adventure episode! It is just so satisfying to watch a computer simulate real life to such precision.
Man, I really enjoy your content. Pure professional and pleasant.
Those fishes behavoir patterns look suprisingly real, this is rather fascinating!
I must confess that thanks to you I have a newfound love and passion for using Unity and Compute Shaders for my simulation projects.
If I may make a suggestion, would it be possible for you to go back to your planet generation code but maybe add a tectonic plates simulation to see how the planet would change its shape with time?
WTF?! yesterday I was thinking exactly the same after watching those same videos. This would add another layer of realism to procedural planet generation. 🤤
@@leecaste I wholeheartedly agree! Though from the few papers I've read regarding that, it seems quite convoluted.
I’m learning to code on my own, and seeing what you can do with it I really motivating and enjoyable ! Thanks a lot , please continue !
You're really inspiring, love these challenging little adventures, opens up your eyes.
I just watched a man man virtual fish and honestly, amazing doesn’t begin to describe this.
This is remarkably good for simulating fish! How interesting!
I don't know what is better : Your animations and teaching, or your ideas and skills. Anyway, you are really smart and entertaining ! I really enjoy your genius videos !
Man maaaann... Your teaching ability is insane. My respect, stunning job!
Definitely try using a discretized vector field for performance gains - divide the space into voxels/pixels and assign a vector to each voxel. Each entity goes to neighboring voxels and adds a vector from the center of that voxel to itself, with magnitude falling off with distance. When a boid tries to find its neighbors, it subtracts its own field from the global field and averages the vectors of its neighbors. This gives a nice "pheromone" style approach like in ant colony simulations.
I think I've just watched the coolest thing of my life.
I`m absolutely in love with this channel, it`s very inspiring and my big thanks to Sebastian!
I'm blown away by how you even find a point to start and then come up with the maths to do it
I got distracted at 3:30 by the mesmerizing way the vortex moved
I love your visual studio colour theme! Which one is it?
Sebastian really makes some interesting and cool videos and makes them look easy using Unity which everyone can get for free. Much respect for this guy.
Simple concept, elegant execution, insightful explanation. Brilliant! Subbed.
8:10 if I could bottle up the feeling of excitement, pleasure, and satisfaction I got when this part came on, I’d be a millionaire. Seriously, well done
I come back here every few months just to hear Seb say 'boiiids'.
Gosh this is so beautiful. I've never seen something like it. Not just a coder, an artist.
maaaan you are the boss !!! Haven't seen anything rapped up that clean before !! thanks for being there !!! 🙌🏽🙌🏽🙌🏽🙌🏽
Whenever I watch Sebastian I realize I am a trash programmer.
But what I have to remember is that Sebastian is world-class. It's like comparing yourself against Usain Bolt in running. Strive to be the best you can be and learn from giants, but don't compare yourself.
What I exactly feel :(
There is no linear scale of how "good" a programmer is. We're all made up of different strengths and weaknesses and tendencies. Sebastian has a very inquisitive and creative mind that drives him to dive deeper into lots of little aspects as many would and finding fun new experiments on the side. And he has(or rather takes) the luxury of having time and allowing himself to go off on tangents which often are rewarded with deeper understanding or snippets that can be used later or for something different or inspire a whole new project.
I don't know what his job is or how much "professional" development he does but in some regards he might be considered a "bad" programmer. When he doesn't stick to a deadline, the scope get's bloated, maybe he has a difficult time concentrating on the task at hand, his code, while creative and doing what it should, may not fit well with others from a team or cohere to certain standards, might lack motivation when the project isn't challenging or interesting. There's just so many aspects and different coders are better suited for different tasks. Find your niche and strengths and decide if you really want to earn money with it or rather try to keep the passion alive as a hobby. Not that it's impossible to work on a passion project and make money with that but that's the holy grail of most professions or activities. Like right as I bought my first DJ equipment, I decided I never wanted to do that for money despite investing money into it. (actually DJed two weddings of family/friends, swearing never to do so again after both :D )
@@simonisenberg4516 I'm honestly saving this for when I need it, nicely explained!
Hey its Cod Ghost and we want our fish AI back.
Every minute of the video, you're going the extra mile. Wonderful!
Bro i just love this channel, for just few days i have learned some goegraphy,coud placement and fluid movment, how birds tend to form shapes, how was terrain formed, how does many cool ways of solving some programing problems work, lots of simulations on some math problems, and sooo on in just few days and it was all while showing us how to program all that and implement into a game, and all this was soooo iterestingly expalied that even i with adhd was soo drawn to his channel more that i would have been to some series, and i nearly forgot electronics how gates work how pc works how graphics card work and not just that but showed you how he learnd it so you can too and show you how to do it your self step by step, i mean im just blown out how usefuul would it be for children to learn from you cuz this whould be perfect knowlage for futre kids.
Coding Adventure Guy: I want to program many individual objects to move around the field as if they were alive.
Coding Adventure Guy, 2 minutes later: haha spirals
5 episodes later: recreating the entire Earth
this comment aged well
@@shifanahmed3990 indeed xD
I remember that when this video came out it was what introduced me and finally helped me understand rays in coding and stuff. This is still so cool to watch!
I'm really enjoying your videos! I'm not a coder, but it's beautiful to see how you play around with the code.
Damn. It took me 12 years to find out.
But now I finally know the meaning of half of my nickname.
That raycasting object avoidance solution seems really performance intensive
I wonder if there is a better way
Maybe you could loop through all nearby objects (using the spacial partitioning scheme shown in the video) and just calculate the distance and angle towards their center?
more intense than twice your existence
@@ThePC007 looping is pretty intensive, the less you can do the better.
The best solution for performance is to calculate the raycast vectors at the start, so that you only ever have to calculate the directions once.
Then, whenever a boid checks for a direction it's not doing all the turn fraction stuff and instead is just looping through an array of vectors.
You can also adjust how many directions would be generated at the start if you wanted a less detailed obstacle avoidance, decreasing the amount each one would loop.
The most performance intensive part other than calculating neighbours is actually iterating through each boid and applying their new movement vector.
@@bearwynn If you use the partitioning scheme the looping shouldn't be _that_ intensive and depending on how you store the coordinates of the boids (preferably in an array consisting of only the coordinates themselves (and not a pointer to their object or anything)), then you could loop through them with very few cache misses, which would make it pretty fast. Calculating their distance and angle should be fast as well, since (I believe) you could even drop the square root part of the distance formula entirely.
There aren't many optimizations if we want to keep using rays in a classic "does the ray hit the triangle" way.
But in this case we don't really care about precise surface collisions, just a rough idea of whether or not e.g a random background fish is about to swim through a wall or something. So we can optimize this significantly by by precomputing a 3D grid or octree and simply marking a given cell as solid or empty. Now we only need see if a vector passes through any solid cells, which is much easier than looking for ray-triangle intersections.
Of course, once we have a simple integer-aligned grid like this, we can make a bunch of additional assumptions and optimizations. But I'll leave this as an exercise for the reader.
I have always been fascinated by boids and recently became enamored with spatial partitioning techniques. Great video
Very nice. I find very amazing that you can combine Math and nature. It seems so fun and interesting to watch you.
[Dunkey Voice] Procedural Subnautica baby!
Wow! Amazing video. I love those coding adventures. I've got 3 questions:
1. Wouldn't it be easier if you used the Job System instead of compute shaders?
2. Where do you get the ideas and inspiration for coding adventures?
3. When is the next episode of the neural network series coming?
It definitely wouldn't be faster using JobSystem. It spreads things on CPU Threads. There are far more on GPU.
The rest of questions... I don't know :D
@@AramilAnakir Thanks for the answer.
The Job System is definitely easier than compute shaders. It's also extremely fast when using the Burst Compiler. Compute shaders still have the potential for much more performance, if done right. We're using the Jobs+Burst for the same thing (but not entities), and using compute shaders for occlusion and indirect instanced rendering. I've been wanting to move the Boid code as well but haven't had the time. Right now I can get 50k+ fish reliably, I'm temporarily blocked by some data copying (yeah, take time!) and a bug with the GPU sorting that limits me to 65k instances for now.
Here's an example of how our game looks: media.giphy.com/media/2xEAuD1mqqjk7ul1Pp/giphy.gif
Beyond Blue is an underwater exploration game releasing this year on PC, Xbox1, PS4, and on Apple Arcade, if all goes well :)
Come follow us on twitter.com/BeyondBlueGame
:)
@@noamweiss2244 Woah! Such a smooth transition between answering a question in comment to promoting your game. You clever.
Very inspiring to watch + cool result + cute dog profile picture = perfection.
Thanks for creating this
The coolest coding video I've seen thus far. Great work!
Hi @Sebastian, don't know I you ll read this, but I just loved the ending, going from completely off track abstract Fibonacci sphere to... Actual usage for fish behavior! Just drop my jaw! I loved both the idea and the result.
Enjoy your deep sea journey :)
🕊️ => 🐟 🐠 !? 🤯 ... 😍
I'm gonna stea- COUGH COUGH I mean cop- COUGH COUGH I mean look into this on my own and make my personal* implementation.......
Well I mean most coders aren't afraid to say they borrowed a few ideas from here and there. Especially if it's free to use. Why build say an entire system from scratch when someone has already done the feature you want?
@@genericytprofile852 true, but it's also bad practice to copy entire sections without understanding them ;)
This is very sophisticated explanation. Its pleasure to listen your voice
That's gotta be one of the coolest programming projects I've seen, gonna try this now thanks
Usually when watching these videos, I do not understand half of what he says. Does it get better over time?
Still, they are very interesting to watch.
I swear Sebastian. You could recreate the universe if you tried.
Make a randomly generated spherical planent (which you've done), add an also randomly generated ocean (also done) apply Darwinism to the fish you've made. Calculate your rain water erosion with real time clouds and plop a third person character on said planet.
Combine all the things you've already done and you've got a game far better than all those AAA games. Make it an Rpg simulation game charge $20 and you'd make millions.
You've been my coding hero since High school. Keep at it, your videos always make my day :)
From start to finish, every bit of this video was impressive.
These things are so fascinating, i love these series
0:13
No one:
Touhou players: put their cursor on the screen and start dodging
As soon as you said "a nice irrational number" at 3:01, I thought instantly of this Numberphile video : th-cam.com/video/sj8Sg8qnjOg/w-d-xo.html
There is an immense overlap between this aspect of your direction-picking function and that video. And, the Golden Ratio is in fact *the most* irrational number, and that Numberphile video explains exactly why (watch all the way to the end). I'm mentioning it because of your clearly evident joy becoming sidetracked by the beauty of the underlying math. (100% with you on that, by the way!) Cheers!
That's exactly the video I thought about lol that was one of the best Numberphile videos imo
Not sure why this popped up in my recommendations, but it's actually very useful to me. I haven't looked up coding or math videos in a very long time, but today I'm doing some programming on a project involving lighting and the point distribution stuff will be very helpful to me. Thanks for uploading!
I don't know why, but when you said you were going to swim with the fishes, and the video cut to you actually swimming with them I felt an immense sense of hapiness. This is a very nice video, keep it up!
5:44 looks like the start of some pretty cool spiral galaxy rendering. Maybe a future part of your solar system series?
People who watch JoJo already knowing about the golden ratio: The kool kidz
th-cam.com/video/tLyRpGKWXRs/w-d-xo.html
normal people who already know about the golden ratio because its the most common ratio in nature and commonly taught: shut up you are special for watching a shitty anime
@@seniorvenusdigital3904 tell us why jojo is shitty
Godamn, this is so cool. Lovin’ this coding adventures man, awesome work👌👌
I love your work. So clean and elegant.