Create Mandelbulb Fractals In Blender Eevee

I recently uploaded a video of a three dimensional fractal I rendered in blender and a bunch of you asked me how I made the fractal is called a mandible which is a three dimensional version of the modular data set so in the first part I'll be explaining the history and the math behind fractals and then the second part will be the blender tutorial if you want to skip the first part just go to the timestamp on the screen now the concept of fractal geometry has been around for a while but the first time factors really entered the public's conscience was on March 1st 1980 and Benoit Madrid rendered his equation for the first time he based his formula on the works of a French mathematician Gaston Julia came up with a similar equation more than half a century before mandalas unfortunately usually I would never get to see his work visualized because to fully capture the detail of these kinds of fractals you pretty much need a computer because trying to draw it in paper is nearly impossible due to its incredible complexity that's why surely I could only speculate what this formula would look like even monopole was only able to render his formula because of his job at IBM where he had access to very powerful computers this all makes it sound like the formula is incredibly complex but it's really not the entire formula to create a Mundell both Z equals Z squared plus C in this formula is Z and C are complex numbers so a complex number is a number that has a real part this number could be any number that you could think of negative numbers positive numbers fractions anything really the other part is called the imaginary number now this name doesn't really make sense because the imaginary number isn't imaginary it has a value which is the square root of negative 1 but because there's no real solution for the square root of negative 1 it just assigned that the unit I and call it imagine this means if we square I we get negative one this is going to be a big part of the fractal so to created it we'll just make a normal plane and assign all the real numbers to the x-axis and all the imaginary numbers to the y-axis now any complex number has a point on this plane so now what we can do is take any number from this plane and insert it into our formula now to get a result you can try to remember how to solve an equation and how to simplify it that's a lot of effort so I found this website that lets you solve complex equations and even shows you the steps it does which is really interesting because it gives you insight into how the whole mumble set really works so now if we insert our point into the Z and the sea of the formula you'll see that the result is an entirely new point now the cool part is that we can take the result and replace the Z in our formula with our new number and you'll see we get another new complex number and we can do this over and over again iterating the formula if you repeat this for all the points on the plane you'll see that they all fall into one of two categories either keeps moving away from its original point towards infinity or it stays within two units of its original position and to get the funky psychedelic colors you've all seen in the monopole set all you need to do is color the points depending on how fast they move away from their original point [Music] but we want to make three-dimensional factories so on August 11th 2009 mathematician Daniel white posted a blog post where he wrote about his discovery of a three-dimensional version of the mandible set and he called it a Mandal bulb now to make this he didn't use the traditional three axes X Y & Z to make the fractal but he used spherical coordinates these used two angles and one radius to describe the location of a point now these things look so cool they've even been used in movies like big hero 6 or annihilation and you can also recreate them and lend their to make the fractal I'll use the newest blender version 2.8 which is currently solon alpha so expect at least a few crashes along the way the reason I'm using this version is because it has a new render engine called Eevee this lets us view the the fractals in real time I'll create the fractals using volumetric so for us to see them in the viewport we'll have to enable volumetric here and under here you can see an option called volumetric shadows it will help us a lot later on because it will let the volumetrics interact with each other so it doesn't just look like in the morphus blob but actually like a solid object we can ignore the rest of the scene for now and just keep the cube and open up the shader editor basically we just need to replicate the formula from the blog with math nodes so to get the x y and z variables like in the formula we need to create a texture coordinates node and a separate XYZ node of the object into there so we have our x y&z and the first component we need is the row which is basically just the distance every point has from the center of the scene this is also known as the length of a vector so to get the length of a vector we need to create a math node and select help up our and type in two so we square the number and we want to repeat that for the XY and Z and add them all together and then you need to get the square root of the whole thing in the end to get the square root we can take power again and because the point v power of any number is also the square root of the number so we can just keep it like that and now this is the length of the vector of every point in the object so we can just take all of those make a group node by pressing ctrl G and plugging it into the output and typing in vector length this is just for clarity so we can see what we're doing and we can name the group vector in length and this is also our row so I'll just make another node group and call it row just to keep track of what we're doing now the next part is theta which we'll need another separate XYZ node form and now we just do the same thing we replicated exactly what we see in the formula with math notes now we can turn this back into a note loop again and call the output theta and call the little-known loop Clayton just to keep track of what we're doing now we need to make Phi the same thing again separate XYZ note you just try to replicate the mathematical operations with math phones so we divide and an arc tangent for the arctangent though you can just leave this value at whatever you want because adjusting this value doesn't affect anything at all no a group again but then the output fine now you have yourself the components you need to make spherical coordinates now an important part of the formula is the N which basically determines how many bulbs the the big bulb has on the outside so how many I guess blossoms it kind of has so to make it placeholder for that we can just add a value node this will be RN and something we need to use over and over again is row to the end power so we'll just create a other math node power and put Rho on the top and in the bottom there you go so that will make the x y&z parts of the formula so again we'll just have to recreate all the operations with nose [Music] [Music] now this will be our X component and to make a note group of this first all create a reroute here by a shift left clicking and dragging to create this little socket this is helpful because if I didn't make that it would create two inputs for the end which is which we don't want this way you can see this is inside and it only has one input and that makes sense and I can name the inputs and in the panel down the side which you can finally open and close by pressing n give it a naval color you can make it red just to make the whole thing look a little cooler now if ey component is almost the same so we'll just copy that and to make sure that we don't overwrite it you can press this little - to create to make this its own user then you can type in Y and make it green because Y is green now the only difference between the X and the y is that the cosine here is also assigned now we can rename the outputs y there you go now you have your X and your Y all we need now is our Z which is the shortest of the three so we're almost done with with all the math notes [Music] you make note group again call the output Z and the inputs here are we have our N and our theta phase and bottoms theta and this one end there we go so that's our x y&z outputs and to finish this off we'll just need to multiply the x y&z with our power R up here [Music] and now we can combine this all back to a vector now because this is the main part of our formula we can turn this all into another node group so let's just take this over here shift left click again to reroute so we can get it all nice and clean and select all those parts press ctrl-g put this into the output now this is the output of our z component in our formula so this is the thing we'll keep plugging back into the next iteration like we did with the mother pulled before so we can just type in and see you there and the inputs are going to be N and Z so basically the way we'll do that is well copy the node group over and over again plugging the Z output into the Z input again and again if you remember in the two dimensional formula in the end we added the Seebeck onto it so too bad we'll add a vector math phone and add the original point back on syrup like that now it's a good idea to make another node group out of this because we'll be needing a few more inputs and outputs to get this to do what we want so this vector is our C so I can rename that to C now we'll need to add a lemon input which basically decides how far a point is allowed to move until it's not inside our bulb anymore so I'll just add you just try guys drag that and today no I guess not that's difficult because if we add another one it makes this vector input which is not what we want we just want the belly input so we'll have to remove that and add something with a just a value input here and it sucks I wish you could change the type of input each socket is but you'll just have to live with the workaround like that and this is going to be our limit limit will need a length and a iteration counter now to the iterations we'll add one now this gets interesting when you copy open the loop over and over again and it keeps adding one on to the iteration counter so it knows exactly how many iterations it has done and we can color the different points according to how many iterations it took it to move a certain amount which gives us the cool psychedelic colors again so we'll just add one now when the the distance of the point after it's iterated is further away than our limit we don't want it to be inside our bulb anymore so we can decide that by taking our limit and adding a less than node [Music] [Music] we have to put the limit in the bottom there and this returns a value of zero if a point is less than the limit and the value of one if it's more so if we multiply this with our iteration counter then basically just gets rid of all the values that are outside of our limits anyway so this is our iteration so we can plug this into the output again call this deter to get the distance of every point from the center of the scene we'll just add our handy vector length no we made earlier by going to the group right here and adding our vector length if you've named it like I have they can just plug the output of the ad into there and this will then be our vector let me just call it length sure and now we want to keep the limit and see and then this is going to be our Z the output of the ad is going to be our Z and then we want to keep the ending so now it's sort all of these like we have on the other side so it's going to be easier to copy the whole thing and that's basically it now we just need to iterate it by copying this over and over again and plugging the outputs of one into the inputs of next one so let's do it about five times first to test it see if it works [Music] make sure not to mess it up like I did there plug the right outputs and inputs otherwise you will get a mess in the end so now all we need is a volume metrics known and plug the iterations into the density and plug that into the volume output done to the surface into the volume of the material output and now let's just the end so about eight and right now you can in blender two point eight adjusting this doesn't do anything so you'll have to add a value of node to be able to adjust inputs here which is a little weird they'll probably fix that pretty student hopefully so now if we render this by pressing shift Z we can see an amorphous blob now this looks like crap because the lighting sucks at the moment so if we move our point like we have here a little closer and increase the strength you can see something happening in there now to get rid of this outside mess here you can add an a greater than code lab greater than and plug the iteration into there I'm trying let's say three point two five and there you go now you've your mando bulb isolated at the moment this looks very low-quality so let's just move the camera a bit closer just to see it and then you can adjust the tile size here too - now you can see you get much finer detail around the edges there so together looking a little more dense you can add a multiply node and turn that up and there you go now you have looking a little more solid can't read the background off no this is where the creative part comes in you can now just adjust the light to whatever you want I'll just make some area lights now the way you can animate this like I did is by adjusting the end value over here with higher values you get a lot more little tiny bulbs on the outside with lower values you get less bulbs on the outside to get better quality you should adjust the V start and end because that basically tells wonder how far away from the camera to look for evolving metrics so if we turn this down to as small as possible without without the bulb completely disappearing you'll see that the quality is a lot better another important part in making this looking good is it adjusting the shadow sample to give it you can see if it's very low it goes back to looking like in the morphus blob and not like it beautiful fractal so if you turn this higher up you can actually see the detail emerging again and this seems to have fixed our lighting problem a bit now to make the cool colors and to give it some cool colors and not just the white cloudy look we can add a color ramp if we adjust the color ramp to HSB hue saturation value and change this too far make it red and blue you can actually see you have yourself a little rainbow now if you take the length output and put it into the color it's sergeant CIE color itself and you can see it look it looks kind of like a nebula or something it's a it's a pretty cool effect actually I had a slightly I'd slightly different settings for for the one I use for the video I think I had this one a little more purple and this one blue but you can see you can play around with this forever and find new cool looking at ways to make a make this but basically that's how you make a manual bulb and blender you can use the same technique of replicating the formulas using map tones for basically any a geometrical equation you can find out there so I hope this was at least a little helpful and if you ended up making something cool with this I'd love to see you can send it to me on Twitter or in the comments below if you don't want to go through the trouble of creating all these math notes and everything you can just download the original file for the video I made in the description below if you just want to play around with it or create your own cool effects

Channel: JonasDichelle

Views: 182,610

Keywords: blender, tutorial, fractal, mandelbulb, mandelbrot, set, julia, how to, cg, volume, eevee, math, learn, pi, annihilation, big hero 6, movie, vfx

Id: WSQFt1Nruns

Length: 21min 53sec (1313 seconds)

Published: Mon Jul 23 2018

Reddit Comments

[u/Richardiovascular]

Yes! Thank you, this is amazing, well done.

[u/Chaotic_Apollo]

I normally watch blender tutorials while at work with no sound just seeing people build stuff. I have no idea what the hell just happened here. This is great

[u/nothereorareyou]

Fascinating! I'm tempted to download 2.8 to try this out.

[u/Alexander_Sokerov]

I am stunned...WOW.

[u/goffley3]

Nice job! I'd love to try and make clouds from this.