Wednesday, July 6, 2011

Mandelbulb 3D Tutorial: Different 3D Fractal Formulas and Hybrids

... or "formulae", to be truly correct ;)

Up until now, you've been working with the formula that loads on default when you open Mandelbulb 3D, that is to say, the original one:

Formula Tab Window

But just like 2D fractals, the possibilities in the 3D realm are also infinite.

The challenge is to find formulae that are aesthetically pleasing as well. Of course, actually coming up with mathematical formulae is beyond me (for now, I tell you!). Lucky for us, Jesse built in a Formulae tab in which he has programmed many, many different formulae, from different sources:

As you can see, you can use up to 6 formulae. What this means is that you can combine different mathematical formulae to create a new, unique 3D fractal. But before I get to that, let me show you a few examples of single formulas. 

As is visible above, the default formula that loads for the default 3D Mandelbulb is "Integer Power". Notice that there is a little black dot inside the "Formula 1" tab. This means that it is active..

To choose a new formula, you simply drag the mouse over one of the buttons (3D, 3Da, 4D, 4Da or one of the adds) and choose an option. Note that any formula name that begins with an underscore (eg. _ptree_tess) is an add-on only, and won't do anything if you load it by itself. They are meant only as modifiers to actual formulas. Ok, here are a few examples of interesting looking formulae (in some cases I rotated them to show them off better, click to enlarge):


There are of course many more. But these are just the beginning, for several reasons: First, as I've already said, you can make a hybrid fractal using two or more of these formulae. To do this, just go to the next Formula tab in line (eg. "Fo.2") and choose a different one, and then click on "Calculate 3D" to see what you get. In some cases you may have to zoom in or out. Here are some examples of hybridising formulae:

Mandelbulb with ABoxVaryScale
ABoxVaryScale with Beth1522
CommQuat with IQ-bulb
Beth1522 with CommQuat

The thing to remember is, just because you get a pixelated noisy mess when first trying a hybrid does not mean that it is worthless. Explore it a bit ;) ... Some really are just noise everywhere, but with some, if you play around in the navigation window, treasure mines of beautiful 3D fractals can be found. One such example, I have found, is combining "Bulbox" with the add-on "_AmazingBox" .. This is what you get:

But from here, I zoomed in. And I found what I call, 35th Century Earth ;) ... Apologies for the time it's taken to get to this Tut page. Lots happening in my life right now.

If my tutorial is helping you, please consider supporting me over at my Patreon page.
I also have a deviantArt gallery.

Go to the next Tutorial page - Mandelbulb 3D Tutorial: Cutting


  1. What a cool bunch of images... ABoxVaryScale reminds me of a Volvox algae.

    What are the system requirements for Mandelbulb3d, and about how long does it take for the images to render? I'm considering downloading it, but am not sure my somewhat-old computer could handle it.

  2. Hey Emily :)

    Well, everything you see above renders really quickly. Those are simply print-screens after I've rendered the formula in "Preview" mode. What takes long is once you've zoomed in, found a nice looking spot, and want to render it with as much detail as possible. Then it takes anything from 5 minutes to half an hour (so far with my experience). But I sometimes see the guys over at fractal forums talking about "overnight renders" of 10 hours or more! And most of them have pretty good PCs.

    I recommend you download it anyway and check things out :) ... I'll make a "Downloads" page soon but, you can get the latest version of Mandelbulb 3D at :)

    Here's a direct link:;sa=downfile&id=23

    1. I once rendered an image for three days and only got three pixels. I turned off the computer and did not mess with fractals again for another 27 years. Computers are slightly better now:)

    2. You can speed up things when using SSD drives. They are no more expensive and there are even some that you can attach by an USB3.0 plug.

  3. More invaluable information. As we say in my native Slovak, "Veľmi vám ďakujem" [thank you very much]. The learning curve has been steep, but with your assistance I am finally producing some images that I really like.

    Hope that you don't mind that I suggested your site as a source of Mandelbulb 3D tutorials and information in my blog:

    1. Hehe... Do I mind, you ask... =P .. That's great! Veľmi vám ďakujem! ;)

      I'm really happy my tutorials are being so useful to you... When you've done a few pieces that you're proud of, please post them somewhere and give me the link, I would really like to see them!

  4. I tried the combination you mentioned in your tutorial and could find nothing. It was an unnavigable fractal. The controls are haywire with that one.

  5. how to i get more formulas for different looks? i feeel like i have a small library