Simple Fractal rendering

[@OlofNisshagen]

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

[@Breuhh]

Exactly

[@neon_Nomad]

Fractal worlds?

[@יובלהרמן-ח2ד]

If we are already comparing I like this channel better! CPP and sdl all the way!

[@EpicVideoGamer7771]

@@יובלהרמן-ח2ד SFML not SDL

[@duality4y]

100%

[@owlroseproductions8876]

You are a gem in the programming space of KZbin. 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

[@spaztor7723]

where does an idiot such as myself begin in making somthing like this, a hobby??

[@owlroseproductions8876]

@@spaztor7723 well, as a starter for visualizations like this I recommend processing/p5.js. it's not the fastest, the sturdiest or prettiest, but the ease of use is unparalleled. I have spent countless hours in it and I've loved every second

[@Jake_Gotthard]

@@spaztor7723i dont even know what “constant;” does but i have adhd, autism, the determination of someone trying undertale for the 1st time and doing true genocide, an ungodly amount of love for cool stuff like fractals, a BEAST of a computer and i am going to do this.

[@karolciszek8550]

That zoom with the music was just magical

[@_miobrot_603]

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.

[@therealsemechki]

Good luck on your journey! If I were to make a suggestion, use a language that supports multithreading, like C++! Or, you could learn a shader language🙂 (GPUs aren't *quite* as bad at using double-precision as it might sound, although they are still pretty slow at it. There are techniques to mitigate this, though!)

[@karolciszek8550]

You could absolutely plot a Julia set like this in Python. It would be a great project for a high school student. Good luck.

[@blaze_arch6864]

Try Nim language Nim has syntax of Python And speed of C

[@josephastier7421]

Go for it! The output of these fractal images looks really complex, but the math is simple. Some of the biggest bang for the buck is to be had displaying a color palette instead of a grayscale gradient. Then your renders will come to life.

[@thecakeredux]

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.

[@mmd-wt5eq]

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

[@PezzzasWork]

Thank you!

[@brayden1562]

Came for the programming. Stayed for the existential crisis.

[@chochochon5464]

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

[@fabienherry6690]

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

[@jonasdaverio9369]

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

[@AiRde]

Yes this is the methode use by Kalles Fraktaler, an amazing fracal render

[@jonasdaverio9369]

@@AiRde I once tried to implement but the result was awful and glitchy. I would really have to make something smarter to pick the point.

[@thingthingthingthingthingthing]

I used that for rendering Mandelbrot set, but only the center part which takes the most time

[@dasjulian3]

Fractals are quite nice.

[@stchannel3648]

Yes.

[@PezzzasWork]

For sure

[@dacolib]

Definitely

[@marcusmelander8055]

Indeed.

[@stevenbmeza]

absolutely

[@2_Elliot]

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

[@jaydevsr2536]

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!

[@ajs1998]

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

[@doggo9757]

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.

[@crackedemerald4930]

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.

[@spudd86]

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: kzbin.info/www/bejne/hnWUi5-hg8tqfbM It's open source so code is at: github.com/Spudd86/julia-vis

[@jonasdaverio9369]

Oh, you didn't write in Julia... What a missed opportunity :p

[@spudd86]

@@jonasdaverio9369 Julia didn't exist when I started...

[@Tann114]

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

[@PezzzasWork]

Yes I was very surprised myself !!

[@kubstoff1418]

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!

[@kalelsoffspring]

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

[@tjavado]

this is actually a julia set of the mandelbrot iirc

[@kalelsoffspring]

@@tjavado yeah, that's what was said in the video, I just thought it was a nice alternative. Tbh I probably would've clicked off if it was Mandelbrot again :P

[@vitalys5076]

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

[@Maus_Indahaus]

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

[@Ener-G]

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!

[@tm001]

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" 😎

[@WorldWeaver]

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.

[@firkinflamer8604]

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

[@Delta0001-y]

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

[@puddleglum5610]

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.

[@Henrix1998]

There's some compiler flags that probably could make use of SIMD without any extra effort

[@puddleglum5610]

@@Henrix1998 unfortunately, its too complex for compilers to translate into SIMD instructions as you have to change the code logic quite a bit from regular Mandelbrot code in order to make full use of the SIMD instructions

[@user-sl6gn1ss8p]

@@puddleglum5610 Maybe by creating a "computeNextFor8pixels" which does just that (taking also 8 times the input and returning a struct or something like that), and turning optimizations up? I've had good luck doing that with random number generators (like pcg64), don't see why this should be any harder for the compiler.

[@INT41O]

@@user-sl6gn1ss8p Just use SSE/AVX intrinsics, not too complicated in this case. If you have to rewrite the code just for the compiler to better optimize, you might as well optimize it manually.

[@user-sl6gn1ss8p]

@@INT41O fair enough, I'll look into it

[@saniancreations]

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

[@PezzzasWork]

:D

[@novygaming5713]

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.

[@crakhaed]

Lol I thought this was a mandelbrot set until this comment 😂 ty for teaching

[@hippopotamus86]

Perfect. Love your work.

[@wallywutsizface6346]

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).

[@crakhaed]

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.

[@QuentinVaresano]

Your videos go better and better, please never end

[@absence9443]

Definitely need more simplified coding channels like these!

[@novygaming5713]

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.

[@eugienepeters1608]

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 :)

[@bergolho]

Congratulations on this awesome video man!

[@CelestialityRW]

Videos like this make me want to learn C#

[@RayznGames]

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

[@tonyb5536]

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

[@mathman0569]

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

[@PezzzasWork]

Thank you! I’ll do my best :)

[@Msatthew]

Well, that last bit was existentially terrifying. Bravo!

[@Graverman]

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

[@raushankumar2336]

This is absolutely dope👌

[@blumbomium]

Might have been the quickest 11 minutes of my life

[@Micro-Moo]

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

[@DRUYD]

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

[@guigazalu]

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

[@brynshannon6692]

the infinity of cosmic shrimp

[@imnotjesper]

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.

[@IncroyablesExperiences]

Toujours aussi intéressant 😉

[@sickbale]

That's pure madness. I love it.

[@84homey]

Beautiful fractals. Beautiful numbers.

[@zelimirfedoran9720]

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

[@guigazalu]

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

[@enzoharquin1543]

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

[@Syp64]

Thanks for sharing this. Hope this inspires future talent!

[@BuffRobotiX]

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

[@MxMxffin]

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

[@zetmor1337]

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

[@BarneyCodes]

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!

[@kaiprzadka6896]

Is there anything like fixed precision? (Python for instance has the decimals module for that)

[@BarneyCodes]

@@kaiprzadka6896 Not as far as I can tell. Since I made mine with JavaScript, and therefore WebGL, the specification for GLSL is pretty bare bones (it's not even required by the spec to have high-precision floats!). I'll have to look into it further though, thanks for the lead!

[@ladyravendale1]

@@BarneyCodesMy first instinct is to preform some terrible bodging with frankensteined ints or arrays to make a very slow but functional high precision number.

[@BarneyCodes]

@@ladyravendale1 I had wondered about trying that too, even just somehow trying to use two floats for each number (two floats == double precision right??).. Haven't actually attempted it though. Let me know if you give it a go!

[@ladyravendale1]

@@BarneyCodes I most likely wouldn’t use two floats, instead just a bunch of ints. I can’t really imagine how you would string together floats for higher precision since by nature the decimal point floats, and since you would have 2+ I don’t really see how that would work. A big issue with most non int numerical classes in JS type languages is a lack of easy bit manipulation/reading. At least to my mind it would be far easier to use 1 int as an x bit mantissa, then however many more ints as the actual value. Write some bastardized version of the normal float implementation, treating your ints as registers, and there you go.

[@shadow-ht5gk]

Your English has improved so much since the phalanx video

[@cmilkau]

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

[@nikitademodov3446]

Nice video! But I don't understand why you resorted to CPU execution.. Most GPUs actually support double precision (at least all that support OpenGL 4.0.0 [natively! looking at you, Apple M1 :/]). I wrote a clumsy unoptimized fractal renderer once too and it ran flawlessly on GPUs (smooth motion/zooming) with full double-precision (max zoom ca. by factor one quadrillion) and I'm sure there's some optimizations that would make it much better if I had the time (and intelligence) to implement them. Anyways love how polished yours turned out! Congrats on (almost) 100k!

[@Pyrografpl]

Nice! I always wanted to code my own fractal diver

[@Pyrografpl]

You inspired me that much so I just finished my Julia explorer in C++SDL. It is 1am 😅 with 16 threads on my i7 6gen it is not super fast. I have idea of caching images and showing them until next frame is finished being rendered. Bit it wont help with animated fractals.

[@Dricou61]

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

[@АлександрТарасов-щ1г]

Кажется, я заглянул в бездну.

[@olbluelips]

I never get tired of fractals!

[@multiarray2320]

is it true that there is a chicken at that point in the fractal, or have you edited it in?

[@d00dEEE]

I believe it's chickens all the way down.

[@mayankthakur2158]

absolutely amazing video, very cool stuff !!!❤️

[@killyGHILLIE]

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

[@groverkiinmuppetborn714]

Thanks! I can now make my own memetic agent

[@crakhaed]

Just wanted to say, incredible username and good luck

[@clementdato6328]

Impossible. I don't believe you can zoom in and actually find a Pezzza's Work icon in the Julie Set rendering. And it prints out exactly "Thanks for watching!" right when your video ends. I refuse to believe.

[@otrocanalmas8096]

thank you so much , sir . this is simply beautiful

[@AbsolutelyPlasmadic]

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 :)))

[@chonnberdosh3834]

In the final zooming-in-sequence the spot seems to be picked very nicely to allow a nice view the entire time. If one ends up in a dark-spot or bright-spot I think zooming in further would be pointless. As I could not see any camera-movement my question is: How does one pick such a spot? Is it just a bit of trying-around by hand until it fits or is there a more clever way to do it?

[@doolee5704]

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

[@don.3s]

I wouldn't be amazed if fractals had something to do with dna and everyone is like a slight variation of a different fractal

[@JakeSeeber]

Beautiful work, thank you for the video pezzza

[@michaellundgren6949]

I feel like you made this whole video so you could put the chicken at the bottom of the fractal.

[@shrimpoffthebarbie]

Not giving yourself enough credit by saying it's simple. Great work. Staring into infinite similarly. Love fractals and will get round to trying program some for myself.

[@Tianeptine1062]

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

[@thatprogramer]

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.

[@cmilkau]

Julia sets, like many other fractals, are highly self similar. I wonder if there have been attempts to exploit that, particularly for recursive escape sequences. Instead of just stopping after n iterations, you could look what number you ended up with. This number could be used as an index into a coarser version of the fractal. Doing this you doubled your number of iterations with a virtually unnoticeable loss of precision. You can also use this technique as a replacement of supersampling for anti-aliasing. Particularly on the GPU, using the pre-rendered version as a texture, this should be highly efficient and simple to implement. Iterating this technique for performance seems straightforward, but requires some extra work. Regions near the border of the fractal can't be used for indexing because complete copies of the entire fractal lie inside a single pixel. On the other hand, regions far from the border are smooth and there is little point rendering them to higher precision. What you want to do is some kind of sparsely populated multiresolution texture, i.e. some areas are low-resolution and some areas are high-resolution, and some areas are "not yet computed". You could fill this by increasing the resolution each time you start over, while only computing regions with unknown behaviour. For julia sets, initially only the behaviour outside the radius 2 disc is known. In the second step, you would calculate one or a few iterations for points inside the disc. If you end up with a point outside the disc, you can update that texel with the new value. In the third step, you know have more known values in your texture. For the others, again you compute a few values until you end in a known smooth area (texel is known and similar to its surroundings) then you can add the iterations of that known texel to the iterations it took to get there, updating the "unknown region" more. As you keep doing this, you increase the resolution occasionally. Now some Julia sets, like the Mandelbrot set, have a true interior (rather than just an exterior and a border). For escape sets, interior usually means convergence to a stationary/cyclic sequence, like the exterior is escape to infinity, while the border is chaotic. In that case you need an "escape" region (a region with known behaviour of the sequence) for the interior as well, because you only want high resolution for the border.

[@travisc8406]

Awesome video! 👍

[@PezzzasWork]

Sorry for my late reply, didn't see your comment! Thank you very much for your support!

[@graham8316]

would be a good explanation of why double precision isn't necessary in most situations

[@fabianportero3563]

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

[@HenrichAchberger]

God makes incredible things I always watch his videos when he makes one

[@brianmiller4614]

The pronoun in the second sentence seems to be referring to God, and it looks like you forgor :skull: the periods.

[@HenrichAchberger]

@@brianmiller4614 this was supposed to offend religious people not grammer nazis

[@michaeldamolsen]

@@HenrichAchberger Thanks, that reply made me laugh way harder than it should have! :D

[@mathpuppy314]

May I ask what platform/language you do all of this in? I really love your projects and ideas and I want to try my hand at some of my own but I don't know where to start.

[@DanDeebster]

Judging by the variables being initialised like i{0}, it's C++

[@daphenomenalz4100]

What softwares and modules do you use for visualizing? I know C++ but never knew how to do stuff like this. Can you make a tutorial video to get it to stuff like this. PLS. Really love your videos. I can probably do this in JS tho pretty hard (i am still learning), by learning the concepts used in this video. But i want to know how to do it in C++ My laptop will prolly blow up tho xD, i don't have any GPU ad its not a gaming laptop lol

[@INT41O]

SDL2 is quite simple to use (it's even in the name)

[@daphenomenalz4100]

@@INT41O thnx

[@StuartGilbert]

That was mesmerizing. What is the music?

[@brianmiller4614]

It sounds like DM Dokuro, but this is the first time I have heard this song.

[@bananadog111]

i love your videos and i'd like to start using c++ as well, but i can't decide which ide would work best, any ideas?

[@anoobis117]

4:54 (makes 420 green). Nice.

[@actravaz]

We did it, we finally found the end of a fractal: *Thanks for watching!*

[@petepete4981]

COOL stuff!!!! Tried to compile your project, but where to get /res? there was a cmake error...

[@PezzzasWork]

There was indeed a problem with the cmakelists, should be better now

[@juh9870_projects]

Is that red halo around white dots on 10:05 a compression artifact, or is there actually a low iteration count in there?

[@Talent_Unlimited]

Those areas have a low iteration cuont...

[@wglint7509]

Hello i love your video and i'm asking what did you use for make animation like 0:59 moment of the video ?

[@trinityy-7]

a fractal renderer was actually the first thing i ever made using a gpu

[@ahuman32478]

Hello Pezza. I built the code you provided on github and got an executable. However, when I try to run the executable, it says I am missing an SFML DLL. I didn't see any DLL included in the github repository. Am I supposed to download the DLL separately?