Mandelbulb 3D Tutorial: The 'DE combinate' button

Right! Back again for another tutorial page. I'm much more experienced now with Mandelbulb 3D, and have thought that I should do a revision of much of what I've already posted, but as that's not terribly exciting, and  as I feel like doing something exciting, I'm going to try out the DE Combinate feature of the formula box.

I learnt about this from two of my favourite 3D fractal artists, Mandelwerk and Bib, through the following works of theirs (and more):

Claustrophobia by Infinite Rooms by Mandelwerk

Two Worlds by bib993

So when I saw these amazing images, of course the first thing I wondered was 'How did they do it?' ... And the answer is DE Combinate. As of right now though, I haven't tried using it yet. I like to keep my first time experiments for when I'm in blogging mode, so that you all learn with me as I go.

My intention is first to try and copy Mandelwerk's "Claustrophobia by Infinite Rooms" and Bib's "Two Worlds" and explain how I did it. Then I'll alter one of them, to test out DE Com features...

Let's go!

Alrighty... The first part was easy. Simply select the DE Combinate button in the formula window (default button is 'Alternate' (as seen above)), and then choose "MengerIFS" as your first formula, and "Integer Power" as your second formula. Click on Calculate 3D and this is what you get:

Next step, use the navigator to face the side of the cube:

Now it's just a question of colour, I think =) .. And, the sides are curved, and Mandelwerk's original has very straight lines... Will try figure it out now.

<...>

Ok, so after an annoying amount of time trying to get his exact colouring, I've given up =P ... But I figured out the curved edges. In the main window, there's a tab called 'Camera' ... I tried clicking the 'Rectilinear Lense' and that did the trick =) ... Then it's just a matter of fine tuning in the navigator and voila:

My attempt at duplicating Mandelwerk's version.

Next, Bib's very intimidating 'Two Worlds' as seen above.

Let me load the two formulae mentioned in the comments and see what I get...
...
Uhm... Ok so nevermind that... =P ... I even asked him for some hints, and he gave me the four formulae he used, but no matter how I tweak the parameters, I can't figure out how he did it =P ... I'm thinking some background in advanced maths may be necessary...

So now, on to some experimentation! I'll use my version of Mandelwerk's Claustrophobia. ... First things first, when you choose DE Combinate in the formulae box, at the bottom of the first formula, this appears:

Just to see what happens, I chose the next option 'Ma' and rendered. As Jesse's little description popup-box says ... "only overlapping parts" .. of the two formulae, that is =) ... After repositioning (zoomed out and rotated) and some minor colour changes, this is what it looks like:

Next, I tried the 'Av' option, and got this (Note, it took much longer to render with this option.) :

Here's a close-up, just to see:

The option 'S1' looks like this:

Then I changed the "Ds" value that appears if you choose 'S1' ... It is 0.5 by default. I tried 0.2 and got this:

Then I zoomed into the center there and did a few colour changes to get this:

=)

And with Ds.= -0.5 :

The option S2 you can check out for yourself... Not much different to S1 but remember that with different formulae, or even just with simple parameter tweaks, results can change drastically.

That completes the DE Combinate tutorial ... Next, I'm hoping to cover that post-process tab ;)

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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