Moin,

inspired by a forum link David sent me, I thought … why not create 3d fractals based on Mandelbrot-ish ideas in Houdini so that one can fly through them?

This is just a default render-out of the point cloud I am creating. There is lots and LOTS of room for improvement - I am just a bit proud to have gotten it working so far. Almost everything is adjustable: Position, size and resolution of the bounding box (which also defines the area of the points to check), bailout and origin-tolerance, iterations.
It's quite fast and since you can move the bounding box through the actual term, you can easily find the sweet spots.

This version does not yet use distance-estimation, it's a pure escape-condition based “on/off” for each point.

Marc

You may be interested in this forum….
http://forums.odforce.net/topic/10207-3d-mandelbrot-primitive/ [forums.odforce.net]

They went crazy in there….some very cool stuff that you may be able to use.

Hi,

thanks - I learned, shortly after I proudly presented my first render-attempt, that there are tutorials on how to “do it correctly”. Sigh :-) But in the end, for me the journey was well worth it. I learned some more math, I definitely learned a bit more VEX and Houdini usage - and a cup of patience.

I'll have a look though!

Marc

Nicolas Heluani
You may be interested in this forum….
http://forums.odforce.net/topic/10207-3d-mandelbrot-primitive/ [forums.odforce.net]

They went crazy in there….some very cool stuff that you may be able to use.

Let me understand this; the first post in that link can be re-created as 3D in Houdini ? First how was it created as 2D ?

Moin,

> Let me understand this; the first post in that link can be re-created as 3D in Houdini ? First how was it created as 2D ?

it's all just math. Entagma has a nice video on creating “Mandelbulb” geometry in Houdini, using an SDF to get higher “resolution” without having to iterate too often:

… of course I only found that video after I created my own version from scratch. But that's the way I learn the most anyway

By changing the formula and playing with the “zoom factor” (or boundaries) of the values piped into the formular, you get varying extracts and/or completely different outcome.

It's not about “how to create it in 2d”, because these formulae are not exactly “this will create a visually pleasing result” kind of things. More often than not the 2d “version” of this specific kind of fractal visualization is not really resembling the 3d “version”. For the “Mandelbulb” the 2d version is the “Apfelmännchen”, aka Mandelbrot set. If you iterate over that formula slightly different (checking individual positions in space instead of distances to the origin), you get the “Julia set”. Both look quite different in 2d versus 3d.

There is a whole community dedicated to this kind of graphics. If you want to learn about the basics, I found this explanation very helpful: http://www.skytopia.com/project/fractal/mandelbrot.html#pandora [skytopia.com]

Marc

malbrecht
Moin,

> Let me understand this; the first post in that link can be re-created as 3D in Houdini ? First how was it created as 2D ?

it's all just math. Entagma has a nice video on creating “Mandelbulb” geometry in Houdini, using an SDF to get higher “resolution” without having to iterate too often:

… of course I only found that video after I created my own version from scratch. But that's the way I learn the most anyway

By changing the formula and playing with the “zoom factor” (or boundaries) of the values piped into the formular, you get varying extracts and/or completely different outcome.

It's not about “how to create it in 2d”, because these formulae are not exactly “this will create a visually pleasing result” kind of things. More often than not the 2d “version” of this specific kind of fractal visualization is not really resembling the 3d “version”. For the “Mandelbulb” the 2d version is the “Apfelmännchen”, aka Mandelbrot set. If you iterate over that formula slightly different (checking individual positions in space instead of distances to the origin), you get the “Julia set”. Both look quite different in 2d versus 3d.

There is a whole community dedicated to this kind of graphics. If you want to learn about the basics, I found this explanation very helpful: http://www.skytopia.com/project/fractal/mandelbrot.html#pandora [skytopia.com]

Marc

That is what is wonderful, the patterns are amazing; simply with math. How did you create your own version, you simply knew what to do off - hand ?

Thanks for the tutorial and the site link.

Moin,

> How did you create your own version, you simply knew what to do off - hand ?

well, “of hand” is not the best way to describe it
I struggle quite a bit when understanding the math I find somewhere - but I use this kind of project to learn new tools. When I learned Fabric, one of the first tools I built was a 3d-interpretation of Julia/Mandelbrot sets, simply setting one of the coordinates by the iteration count (which, usually, gets displayed as an indexed color). Building a software solution to this helps me in getting into the software (here: Houdini) *and* understanding the math - other people prefer bungee jumping or wild water rafting …

My “solution” does not use a SDF (I did not think of that, but that's the nice thing that you can learn new tricks all the time), but only sets points on a “cubed grid” (grids stacked over one another) or deletes them. When I created the image posted at the beginning of this thread, I had no idea about how to render something (not even talking about points/particles) in Houdini (not that I know much about that yet ), so the result may not be as visually pleasing. But *seeing* some result from your experiments is the best motivation, at least for me, so I didn't really care about “appeal”.

The best approach to math-involving stuff for me is to find sample implementations in code. I usually understand code better than math terms, so by “aligning” the code to the formula, I get an idea of what is going on - then I can take it from there, vary the formula and, at some point, write my own version.
For example: I created a gas/smoke solver in Fabric (from scratch). I had an idea of how to do it, but I couldn't make much sense from most of the formulae I found online (only some of them “clicked” with me, but I always thought I was missing something). Then I read the book by Jos Stam and found out that I wasn't missing anything at all, it's just that math-geniuses like to make things over-complicated to keep their caves clean from amateurs :-D So I build the smoke solver based on my understanding. And it worked very well.

So, in short: It's my way of learning tools: Trying to solve problems I don't fully grasp and by that “approaching understanding” and not caring too much about the “unbearable hurdles the tools put up for me” (people kept telling me that Houdini was impossible to learn. By “solving” problems like 3d fractals I can ignore that - and concentrate on the real issue).

I hope this, in some way, makes sense

Marc

I understand, math wasn't my strong point either; due to a terrible array of teachers I was privileged to come my way in the school years. Although as I got older I wanted to understand a little more. I doubt I'll know the complexity of math as Jos Stam (whom I think is behind Maya Fluids and nParticles), although if it came to me over night, it would be great

Do you have something you can show so I can get an understanding from your first example ? Although the Entagma tutorial is wonderful. Do you know how to use ChoasPro ? I opened the program and read some of the documentation I just want to know how to get started.

Houdini is the creme of the crop in terms of 3D, in my opinion. I know you can do alot in the ‘other software’ and it can be a little more forgiving which sometimes we all need or must use, whatever the case may be. With Houdini you do have to do more planning and understanding, atleast for me; why must I need to do A&B in Houdini just to do C and D.

> Jos Stam (whom I think is behind Maya Fluids and nParticles)

… he is. And he is a great guy who definitely does not represent the “mean” image that company seems to have with some people

> With Houdini you do have to do more planning and understanding, atleast for me; why must I need to do A&B in Houdini just to do C and D.

Hmm … I partly agree and partly do not. When it comes to R&D, I prefer Fabric, it feels more “direct” and has a more “programmer's approach” to experimenting. But once you have accepted that in Houdini you basically have to speak four languages at the same time and have no way of making things *simple* - experimenting / trial and error is definitely possible in H as well.

> Do you have something you can show so I can get an understanding from your first example ?

I will have a look if I can find that HIP file and tidy it up a bit over the weekend, then I'll post it here. The core code isn't that different from what the tutorial shows, because it is the same formula. Just the stuff “around it” is mine.

Right now I am trying to create a “environment-aware semit-automatic animation rig” for insects or robots. The statemachine is working, I just have to rewrite the behavior from scratch. This is so much easier in Fabric, but it's a great way of understanding how Houdini “messes up Python, VEX and noodles”. Big fun.

Marc

PS: I haven't looked at the fractal software available, because I am not so much interested in the final outcome, it's the way to get there that thrills me

I look forward to the fractal HIP file as well as your semi-automatic rig

Houdini messes up noodles ?


I won't go into Fabric until I know Houdini and to an extent ‘the other software’ better; by then Fabric may be old news

Fractal software can aid in visualizing or design creation in 3D / 2D. I'll have to try the mailing list

I have put this little project on my list of video-tutorials-to-do, I hope to get it done this month.

Marc

Should've just made noodles