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):

Beth1522

Riemann

GeneralQuat

MagVsXYZabs3

Ikenagabulb

benesi1pow2

ABoxVaryScale

Aexion1

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