Math x Blender 4.1 = EVEN MORE POWER!

Let's dive into the world of attractors again! In this video, we will use the newest Geometry Nodes techniques of Blender 4.1 to optimize the way we visualize math equations in 3D. In an earlier video, we used the popular Simulation Zone to calculate the values differential equations. This was, however, a very inefficient and time-consuming process. But now that we have access to the Repeat Zone and other new nodes added in Blender 4.1, we can make our node setup even more powerful and flexible! Enjoy the video!
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Timestamps:
00:00 Attractive showcase
00:34 Explaining the subject
01:26 Add single point
02:19 Moving point over iterations
05:22 Implementing the equations
12:07 Fixing a scaling problem
12:56 Points to Curves
13:35 Curve to Mesh for thickness
13:50 Bake node for better performance
14:45 Custom shapes for the profile of the curve
17:36 Quick material
18:11 Quick last tips for other attractors
19:06 The Big Nodebook
19:42 Thank you for watching :)

[@cosmicspectrum4507]

For those of you who are interested in understanding attractors on a deeper level look into the mathematical subject of "Chaos Theory" which is a branch of differential equations. The idea known as "The Butterfly Effect" comes from Chaos Theory.

[@mtranimation]

A lot of cool stuff to discorver indeed! :)

[@igormatheus8698]

intricate geometric sculptures surrounded by untouched nature might be my favorite aesthetic

[@Flushable5000]

Just a quick tip when searching for nodes: Use the first letter in every words for the node, and the wanted node will appear first. So instead of writing Points to Curves, you can write: ptc. Combine XYZ -> cox or cx. Separate XYZ -> sx or **x... XD

[@dialac1]

Bro, I have two words to say THANK YOU! I love videos like this where things are broken down so easy and explained step by step

[@mtranimation]

Thank you so much! :)

[@christiangschweng1552]

This is mind blowingly beautiful. Thanks for the deep dive.

[@mtranimation]

Thank you so much! Really appreciate it :)

[@kamaukinyanjui671]

great tutorial... if yr points aren't working out like our Sensei's try checking the type of data being outputted by the equation node groups and ensure its a vector type...You can do this by selecting the output node ,while within your equation group, and under the interface check on the data type of value.

[@ismailabdulkarim210]

Thanks bro. really helped me out.

[@blenderzyx]

Bro, this helped me a lot. My points were not showing and when I checked the equation group output it was float, changed it to vector and now all the points are showing. Thanks alot.

[@averystablegenius]

Beautiful work, Thijs. Your combination of math skills and artistic sense is unique among all the Blender KZbinrs.

[@mtranimation]

Thank you so much! :)

[@petedejager]

Stunning! I also bought your "Big Nodebook" recently and worked through it - for me it was the best way by far to actually understand geometry nodes. Just updated today to the latest version covering Blender 4.1. Keep up the good work!

[@mtranimation]

Amazing! Thank you so much! Really appreciate it :)

[@rekad8181]

for the profile you could also ctrl+click the outer edge, then press y to seperate it then right click and convert to curve. I learnt a lot from your video, thank you so much! please keep it up!!

[@shifathshabbib1867]

I always wanted to create all the calculus I studied and now found someone who explains it, thank you and Blender, I am saving money to buy your book 😁

[@mtranimation]

Thank you so much! Calculus can indeed be so awesome with the right examples :)

[@Playforpay5845]

This is really really cool, can we animate this to form in an animation?

[@144digital]

All I can say is, I love this... Thank you

[@mtranimation]

You're welcome and thank you too! :)

[@A000803323]

to anyone getting a lot of zeros under "position" in the spreadsheet, try ungrouping the node. that worked for me at least. In my experience self made node groups can be a bit finicky, especially when combined with the simulation zone (and now repeat zone too I guess), so it's best to not group anything up unless you're sure it works, and even then I find just framing everything to be the safer bet. Groups just sometimes fail to update or something. I know with simulation zones you're supposed to change a value, but that doesn't always fix the problem.

[@garrysalisbury211]

Excellent tutorial thanks. I have started to make individual node groups for different attractors. The other nice thing about 4.1 is the menu switch node. Line up the node groups, plug into the menu switch node; plug that into the math add node, and plug the menu input node to the group input node. Then you simply choose the attractor you want. Great stuff.

[@mtranimation]

Ohh yes that is a great way of using the menu switch node!

[@sparshtyagi4213]

Thank you so much for this video i love how deeply you explained everything.

[@ahamrtasmi]

Excellent! I just had to update Blender from 4.1.0 to the experimental 4.2 to be able to replicate the nodes. But I think 4.1.1 would have been enough. Thank you for your contributions to Blender. I find them very interesting.

[@mtranimation]

Thank you a lot! Although its always good that you update your blender, you should be able to do this tutorial in Blender 4.1. But if it now works for you than its good ofcourse! :)

[@ahamrtasmi]

@@mtranimation The problem I had with the 4.1 version that I downloaded is that the name assigned to the "Store Named Attribute" node does not appear in the "Named Attribute" node. However, in the experimental version 4.2.0 it does appear. I even downloaded the most recent version 4.1.1 and it also works, so I deduce that it is only a bug in the version I previously had. By solving that problem your node configuration works great.

[@TheAnimeist]

This helped me understand geometry nodes better. Thank you.

[@arcizen68]

Fantastico tutorial. Grazie di cuore e complimenti!

[@StevenRud]

Wooooww, you are an incredible master!!! I’m blown away!!! Absolutely amazing 👍🏻👍🏻👍🏻👍🏻

[@mtranimation]

Thank you so much! 😁

[@blenderzyx]

This is so beautiful. Thank you for sharing this :)

[@mtranimation]

You're welcome! Glad you liked it! :)

[@willhdq]

Absolutely mind blowing video. Thank you so much for making it.

[@mtranimation]

Thank you so much! Really appreciate it :)

[@rensmanders8439]

OMG this is so cooll!! I wish you were my brother so you could teach me this every single day of my life😁

[@mtranimation]

All the love to you man!😝

[@rensmanders8439]

@@mtranimation OMG you reacted!! All the love to you too!!

[@codeitnative2849]

For anyone still struggling to see the attractor build even after changing the iterations a lot, make sure the equation Group output socket says vector and not value

[@katerinaplamenova3237]

Very interesting concept!! Love it!

[@mtranimation]

Thank you so much!!😁

[@lumencg]

Simple and to the point. Thanks a lot!

[@mtranimation]

Thank you! :)

[@youtuberrick2065]

great tutorial but my question is like how do we tackle higher order differential equations like maybe i wanna make a quartion fractal like that is the general process still gonna be the same also do you have a tutorial on those

[@Number_Cruncher]

It's nice to see how ODE flows can be generated in geometry nodes. Thanks a lot.

[@Anyreck]

Well done! Thank you for such an "attractive" GN expedition!

[@mtranimation]

You're welcome! :)

[@abdelrhman_yahia1816]

this man is talented for sure ,great work!!

[@mtranimation]

Thank you so much! :)

[@daniellunazapata4984]

Really interesting to watch and do, I didn't know about the Chaos theory but it is cool too!

[@vinitvaghani2849]

can't wait to try

[@IzzieAProductions]

So awesome!!! 🙌💜

[@mtranimation]

Thankyouu :)

[@graphguy]

One word - Sweet!

[@mtranimation]

Thankyou!! :)

[@kono152]

I'm definitely going to try this on the lorentz attractor now

[@mtranimation]

Nice! How did it work out? :)

[@kono152]

@@mtranimation I'll let you know when I've downloaded blender 4 and tried it haha :)

[@deadsetanime7102]

That's pretty cool.

[@supercad]

Very cool video!

[@mtranimation]

Thank you! :)

[@gordonbrinkmann]

Great work, when someone asks how to implement complex formulas in GeoNodes I usually say, just combine Math nodes and I point at your videos to demonstrate how this can be done, especially for beginners. However in this case to save nodes I personally would have done it differently, but that's not so beginner friendly. Three Vector Math nodes, two set to Scale and one to Multiply: one to scale the Position with -a, then one to scale with 4 and the third to multiply the Position with itself. Then three Separate XYZ nodes and combining the outputs to build the formulas. But this might be less "readable".

[@mtranimation]

That is indeed a good way of doing it and having less nodes! However, this might not be applicable for the formulas of the other Strange Attractors. That is why, for this video, I choose to use this technique :)

[@gordonbrinkmann]

@@mtranimation Yep, sure. And as I said, definitely the way to go for beginners. The good thing about you GeoNodes and math tutorials is that you show step by step how you can recreate even more complex formulas with Math nodes.

[@JoeTaber]

Instead of using a bunch of nodes to represent the formula, couldn't you just multiply the position vector with a matrix to get the d vector in one step? (surely there's a multiply-vector-by-matrix node)

[@mtranimation]

Yes! For the Halvorsen attractor that would have worked indeed! However, for the other attractors this does not always work. That is why I decided to show it like this :)

[@JavierAlfonsoBellotadeFrutos]

Not related to the video itself, but have you seen the effect on the "thumb up/down" buttons when he mentioned them?

[@hirumaw4822]

What an amazing, could you do that with hydrogen wave function? I think it’s gonna look super awesome with more parameters and shape changes

[@vladislav_artyukhov]

Can the math be performed in the scripting area? I think, it can simplify a lot writing formulas.

[@vizdotlife]

This is amazing! Thank you. I was able to get it to work with Blender 4.1. Question. Can we still use the Bake node if we want to animate and add key frames for the shape to change overtime?

[@mtranimation]

Thank you! Yes you should be able to then click "Animation" on the Bake node :)

[@WallyMahar]

Crap I downloaded the older project file... But just following along here. Should I be able to modify it? With what you've done here?

[@flavio8430]

Great tutorial -- thanks for sharing! BTW, I have your ebook (excellent and absolutely mandatory) and noticed that the "Set Curve Radius" node is missing.

[@mtranimation]

Thank you a lot! I checked and indeed the Set Curve Radius node is not there... Thank you for telling me and will be fixed in the next update! :)

[@pastellepuppy]

Is there any way to view your project files without paying $5? I think I messed up something in my equation and it is very hard to use the video to make sure it's all right.

[@PCgmesforever]

Cool video tutorial! Question. Wouldn't it be more performant to create desired amount of points first outside the loop and in the loop only calculate positions needed which would then be set by index of point outside of loop afterwards using set position ?

[@mtranimation]

Hmmm good question! I think it will not matter that much because you still have to calculate the location of 15000+ points in one go so to say. So maybe it will be a bit better but since we have the bake node I think the differences in performance will be minimal :)

[@clampchowder9569]

fantastic

[@kazisafeerzayan8597]

I tried it but mine is just curving a little bit and then going straight. How do I fix this?

[@imaginingPhysics]

That scaling of the differential step seems to be at a weird place in 12:25. I mean, obviously the numerical integration should only scale "the differential step" which comes out of the differential equations. Does it not scale both the step AND the current position the way it is implemented here? Both methods produce attractors but they look slighly different. Which is the correct way? Note: I am just learning the nodes here, it is possible I just dont know how each node works. Anyway, I would appreciate an explanation, thanks.

[@massonnicolas2339]

Great Job keep on Plz

[@mtranimation]

Thank you! I will! :)

[@MDNQ-ud1ty]

So much work to do something so simple.

[@xyzz4544]

very good video

[@mtranimation]

Thank you! :)

[@alvindzaki6594]

finally! theoretical learning in math and physics will theoretically finally pays off! i will theoretically the richest human in theoretical knowledge! theoretical woohoooo!

[@mtranimation]

In theory that theoretically amazing! :)

[@alvindzaki6594]

@@mtranimation a theoretical theory indeed :)

[@jbdh6510]

Windows 11 default background :D

[@mtranimation]

Hahah this made my day😝

[@MScienceCat2851]

how does one make such a formula?

[@Waffle4569]

You'd save yourself a lot of nodes, and probably performance, if you used the vector math nodes instead of rewriting the equation for x, y, z. A dot product -a.(x,y,z) is the same as (-a*x, -a*y, -a*z). y*y is also a lot faster than y^2, because of the way "power" is implemented on processors.

[@mtranimation]

I know :) for this attractor there are faster ways to do it. I showcase it like this so that for other attractors (with different equations) this technique works too :)

[@LeiffNathanAMendoza]

awesome indeed win 11 wallpaper debunked right?

[@original_M_A_K]

i wonder what the result would look like if you only used Fibonacci numbers for the iterations & the golden ratio for the scale ;)

[@gswhitedevil6631]

where you get math formula's

[@mtranimation]

See the link in the description! :)

[@gswhitedevil6631]

@@mtranimation who to put this type of value 0,008 which has ( , ) this in it

[@mtranimation]

In Blender 0,008 would be put as 0.008 :)

[@gswhitedevil6631]

@@mtranimation ok thank you

[@mtranimation]

You're welcome! :)

[@jakebatsuuri]

I double, triple checked every node and connection. but mine is just making a single array of dots. makes me think that my equation is hooked up wrong. but it seems to be okay. this is soooo frustrating! ARHHRHRHHRHGHGHGHGH

[@mtranimation]

Oh no! Is the output of the first named attribute set to Vector or to Float?

[@habdman]

Yeah mine too is having a similar issue whilst having everything pretty much on par to what he showed. Must be some small misadjustement or perhaps just an unchecked box somewhere

[@davef21370]

I can do the same thing just using the screw modifier. I don't mean to, it just turns out like that.

[@mtranimation]

Oh but thats interesting! Do you mind showing how you have done that? :)

[@bigdaddyproduction7266]

Bro the only problem with this book, is that the screenshots are way to blurry.

[@gswhitedevil6631]

can't we give them movements like old one's

[@mtranimation]

Well with the Aizawa attractor it was very easy to just rotate them and it looks satisfying. What you can try with Halvorsen is slightly animate the a-parameter and see what the results are. I do recommend to set the Bake node on Animate when doing this :)

[@gswhitedevil6631]

@@mtranimation thanks bro

[@haipingcao2212]

Can i use this goddamn thing on a goddamn phone?

[@Ervin-fg6xw]

Futhark?

[@techgaming8940]

Make some naruto rasengan using geometry nodes ❤❤❤❤

[@thomaskaldahl196]

a third of this whole video was just translating the equation into the graphical node system. there should be a way to completely avoid nodes altogether and just use a python script for all of this.

[@user-co7zc2wc8z]

Yeah this is much simpler than before, But it's not animated.

[@AssurMediaCompany]

I hate to be the guy leaving a negative comment. But please explain to us how on earth that the people who actually copy paste everything you do, still manage to not get a functioning "attractors" that looks like yours. I have a suspicion that you're changing something behind the scenes so that people try making it for themselves and struggle to make it work, and you use it as a funnel to make them purchase the project on gumroad. I will be purchasing it tomorrow and I'll update everyone here on my findings. I really hope you aren't the greedy kind of person to trick your viewers into purchasing your products...

[@mtranimation]

No worries and let me try to help you because I can really really really really assure you that everything you see in the video is what is needed to create a Halvorsen attractor! :) I do not change anything behind the scenes because I would feel so bad about myself if I would! I recommend especially taking a look at how the formulas are implemented because thats where one small difference can make a completely different result. Same for the scale node between the Named Attribute and the Set Position nodes. Also, make sure that for the Halvorsen Attractor, the first Value node that controls the randomness is on 0.5. Another thing is you can have a look at the values of the Location, Rotation, and scale of the object. Hopefully these are going to help you! If you want you can sent a screenshot of your nodesetup in this chat too so that I can have a look at it. :)

[@AssurMediaCompany]

@@mtranimation Thank you for your reply. I understand what you're saying and I'm glad you're not part of those kinds of people. It's just a weird trend that every time I copy someone's tutorial, I find it looking different than what they're showcasing. But I'll give it another shot and I'll let you know if it fixes my problem. I did notice a mistake, but it still didn't fix the issue of the points going out into the void. Thank you again for your reply.

[@gsestream]

maff

[@MichaelWeizenfeld]

Geo nodes was developed by maniacs...

[@mtranimation]

And it´s taught by crazy men... ;P

[@Stanisslayer]

Math its to complicated subject for me.