You're like a more math-focused Sebastian Lague, great content!

You are a gem in the programming space of KZfaq. You've inspired a lot of other successful programmers on here and also me (just as a hobbyist, but still). Keep making what you love and we'll love it

Writing a fractal render was one of my favorite projects of all times. I hope you making this as accessible as you did with this video opens allows others to experience the awe when their code creates beauty in front of their eyes.

That zoom with the music was just magical

In a highschool programming class right now, and seeing this has raised motivation to the max. Still going over the basics (in python), but one day I will make something like this. Thank you Pezzza for the inspiration and I hope my comment is meaningful in some way.

Since I was a kid, I've been fascinated by the fractals... I could spend HOURS watching zooming videos about fractals XD

The more fascinating thing is your video. Thanks so much for you awesome content.

Your videos are always inspiring. I remember the time I was myself trying to render Julia sets, I was really happy to see the results. I hope other people try this as well as this is very rewarding!

That is fascinating to watch ! I love how the background of the fractal is still indicating some sort of position despite the infinite similarity

Came for the programming. Stayed for the existential crisis.

Criminally underrated, your content always amazes me in its complex simplicity. Keep it up!

I love this, man. Programming is the coolest hobby ever and I'm so happy to be here. Awesome video, keep it up!

That was a very intriguing dive into the subject, whenever you post something I'm immediately hooked to try that myself. Great Work as always!

If you want arbitrary precision while using your GPU, you can use perturbative techniques by computing only a few points with high precision on your CPU, and then computing all other points in low precision on the GPU. Choosing the points is tricky, though

Fractals are quite nice.

I love this!!! Great videos. Love the easy to follow code examples & visual output (like the multithreaded rendering), very cool!

Perfect. Love your work.

Very beautiful video! All the aspects were so well done. Especially underrated is the sound mixing and the music that follows the camera down at the end. Thank you very much for making this! For 11 minutes of watch time it probably took much longer than that to make and produce. I appreciate the time and effort you took.

love this content! Keep improving and it’ll be amazing. Also love when you show all the optimizations you’ve made and their downsides

Thank you so much for this! I'm in a rush but I wanted to express that your simple, straightforward explanation and approach to fractal rendering has opened my mind to the possibility of doing something similar myself! I've been hoping for this knowledge for a long time. Thank you so much for creating this video as a vessel by which I can begin my journey of understanding!

Came across this channel a few days ago, and I must say this is one of the best channels for programming and math. I have an exam, after that, I plan to binge watch all you videos. The Cool Chicken is a very cool guy.

This is one of the coolest things I have ever seen.

Beautiful fractals. Beautiful numbers.

Your videos go better and better, please never end

That's pure madness. I love it.

wonderful content as always, is so well explained it seems super easy, barely an inconvenience.

Congratulations on this awesome video man!

Because of the way our brain processes grays, the fractal had a lot of detail on the borders of the greys that made them very interesting.

My favorite channel. Every video you post makes me at least raise my eyebrows

This is absolutely dope👌

You really had me for a second there with the logo showing up at the end.

I never get tired of fractals!

The one thing that keeps blowing my mind every time in his videos is how he can optimize the shit out of the rendering time with just "simple" logic and few lines of code, and then he basically says "I can optimize it even more but I don't want to" 😎

Definitely need more simplified coding channels like these!

absolutely amazing video, very cool stuff !!!❤️

I love your content, please keep them coming!!!

Videos like this make me want to learn C#

The only thing missing from this masterpiece is a quick zooming out at the end to show everything in its full glory

It is a really nice idea to perform the sub-pixel computations.

mesmerizing!

Well, that last bit was existentially terrifying. Bravo!

Thank you so much for making this video. I was always interested in making a fractal render but just didnt know what to do or the steps involved, I felt paralysed. This was really helpful. I need to learn to problem solve on my own too without being baby fed :)

Thanks for sharing this. Hope this inspires future talent!

I'm amazed about how far double precision goes In comparison to float. Great content!

I have written a program that renders Julia Sets by using texture mapping to do the inverse iteration method. Basically if you compute the inverse of the function and map the entire plane backwards it will eventually converge to the Julia Set. I'm using this for a music visualizer so we blend the frames together and the Julia Set emerges as the points with colour. I have video of it running. I blends a sort of oscilloscope visualization on top of the frame and then uses that as input to do the Julia Set inverse iteration in the next frame. You can see how the copies of the scope shrink and copy around to build up the shape of the set. The nice thing about doing the inverse iteration with texture mapping is that you *actually* compute the forward function to determine the source pixel for the texture map operation, the texture mapping to the output effectively makes it doing the inverse. The other nice thing about this is that precision isn't really critical and GPUs are REALLY good at texture mapping. I have written the same thing for both CPU and GPU (via OpenGL 2.1, so it runs on a potato), can't do a zoom though, the algorithm requires you to keep an image of the entire circle that the Julia Set might be in (that is the same circle you use as the escape radius). I have explained this poorly I know. Video of it running: kzfaq.info/get/bejne/hqphjc-cs8ybd4U.html It's open source so code is at: github.com/Spudd86/julia-vis

Excellent as always Pezzza! Amazing coincidence that there's a chicken in the fractal too.

Toujours aussi intéressant 😉

Ooo pretty colors!

This is so awesome

Magnifique !

I love your content I hope you get more subs and such and I hope to watch your wonderful channel grow

Really amazing work. 👏

Great as always !

i just wanted to let u know that u have my sub :) cause i really liked ur ants and stuff :)) thank u for ur continued dedication to the cause :)))

i love when you upload!

I've always seen Mandelbrot used for these types of videos, very neat to see another type used. The difference in where the pixel coordinates go in the looping equation seems to be the only real difference, being C for Mandelbrot, and Z_0 for this. Very nice video

this is really cool! Thank you!

Beautiful work, thank you for the video pezzza

There's another cool fractal you can make called the mandelbrot set using the same equation. You're currently rendering julia sets. For julia sets, you set c to a fixed position on the plane while changing z for every pixel. Instead for the mandelbrot set, you just set c so it also changes with z. I personally think the mandelbrot set looks way better than the julia sets since it's a combination of all possible julia sets for every pixel.

Amazing video and channel!!! Thanks!!

The fractals here are Julia Sets. If anyone following along wants to generate the Mandelbrot set instead, it’s quite easy. Instead of an arbitrary C value, for each pixel, set C equal to the complex coordinate of that pixel. So, instead of Z(n+1) = Z(n)^2 + C, replace C with Z(0).

looking at this video motivated me to give this a try in python, fractals are just amazing....

You can also pull out an extra 4x to 8x performance (depending on your cpu) by using SIMD instructions instead of your normal floating point math. It’s a lot of effort to manually code with SIMD instructions, but worth it for the better perf.

A quick tip for getting more detail in the fractal: instead of making the gradient have more range, you can just use a mod function or a sin function to color it based on the iteration count. Kind of like how Wikipedia does it.

Incredible 😮‍💨

j'adore tes vidéos mec continue

that's incredible

nicely done, very interesting

I love how the video takes it's time at around 1:25.

Awesome! I’d love to see this in 3d next 😅

This is cool god teir maths. I wish I listened more in school and now I need to become a computer programmer!

absolutely epic

Great content, keep it up mate!

incroyable !!! vraiment impressionant

After watching the video this comment section is continuously zooming out for me. My eyes and brain can't keep up with fractals!

bro you are amazing

magic! thank you!

This is amazing, thanks! more about fractals in graphics please

Awesome video! 👍

Amazing ❤️👏👏👏

You are amazing 👏👏👏

the infinity of cosmic shrimp

I think basically everyone here knows about the Mandelbrot set and Julia sets, but those who don't should check out Numberphile's video about it with Ben Sparks. It's amazing.

Your really good at making simulations! I have a suggestion. You should try making a simulation like the powder toy "TPT" for short but in 3D! That would be pretty cool.

Nice! I always wanted to code my own fractal diver

Your English has improved so much since the phalanx video

Ohhhh cet accent Français je reconnais :) Nice work Pezza !!

Might have been the quickest 11 minutes of my life

OBS video transition examples while explaining the Xaos method? So cool!

Got a loading spinner right at the RIP float moment, which was quite funny xD

It could be so fun to build a game in which you control a character that coule navigate into fractale structures

i made a program in 9th grade creating the mandelbrot set using 255 iterations. it had terrible performance but i liked it. made it with turbo pascal back then

Coule be awsome to see the whole process from code to how to different ways it on screen and different environments

nice video i wish you would have talked about the fact that there was colour banding tho because only 8 bits per channel were used instead of 10 or higher

This is a great example of why double precision is overkill for most applications.

You can use that "smooth_iteration" as an elevation, and render it in (false) 3D

Thanks! I can now make my own memetic agent

Have you looked into using perturbation to eliminate the float issue? I was able to build simple cpu and gpu renderers, but was not able to follow the perturbed maths to get that buttery smooth deep rendering

Kid: "What if it's made of dragons? And the dragons are made of even SMALLER dragons? And those are made of even SMALLER dragons? And it's just that, forever?" Parent: "Fractal." Kid: :O I think we've all asked the "what if it's made of more of it" question before.

Great video! I've made a fractal renderer using a shader in WEBGL (there's a video on my channel if you're interested) and ran into the same issue of not having double precision, I'd love to find a way around this. I haven't tried animating my fractals yet! I'll have to try it, thanks for the inspiration!