Interview with DavidMakin!

David Makin is another fractalnaut who frequently haunts the hallways of fractalforums.com ... Here are his answers to my 8 question interview.

Pandora's Box ~ See more at David's dA page

What first got you into Fractals?

In April 1999 I had some free time and was just browsing the web and came across Fractint.
I had heard of fractals and vaguely recalled some psychedelic imagery being associated with the term but I had no idea what they were.
After using Fractint for around an hour or so I was well and truly hooked on both the Art and Math of Fractals - as with many programmers/mathematicians I was staggered by the (apparent) simplicity of the maths involved in producing such complicated and beautiful results.
In fact it was the second revelatory moment in my life - the first being when I read through a BASIC manual age 20 (1982) after never having been near a computer in my life before.
Almost immediately after trying Fractint (like many other programmers) I set about writing my own fractal software - the now rather outdated "MMFrac" (Makin' Magic Fractals).

In your opinion, which programs for both 2D and 3D fractals are absolute must-have's for any
aspiring fractalnaut?

Interview with bib!

I posted the Interview with Mandelwerk link on fractalforums.com and asked if anyone else would like to answer the same questions. Here is bib's response :)

Underwater Amazing Object by bib - See more on bib's dA page

What first got you into Fractals?

My father bought me the famous book "The beauty of fractals" shortly after it came out, I was 13.
At the same time my cousin who was an Amiga geek programmed the Mandelbrot set in assembler, it was 
fascinating.

My programming skills were not sufficient, so I started to draw fractals by hand, starting with the Pythagoras tree.
I soon discovered an original method to draw by hand the Levy dragon (at that time I thought I had invented a new fractal!)

In your opinion, which programs for both 2D and 3D fractals are absolute must-have's for any
aspiring fractalnaut?

Interview with Mandelwerk!

Temple of Chaotic Borderlines (Won the Mandelbrot Tribute Contestat dA)

The only reason I started this blog 2 months ago, the only reason that I became so suddenly fascinated with fractals, was because I found the 3D fractal art of Mandelwerk on DeviantArt. After going through almost his entire gallery, I got really into everything, discovered the maths behind 2D fractals, and eventually downloaded Mandelbulb 3D to try some 3D fractal art of my own :) ... (Go to Mandelwerk's Deviant Art Page to see more images like the above)

Then I decided to ask him 8 simple questions, with the intention of blogging them, and he graciously answered them for me:

What first got you into Fractals?

Mandelbulb 3D Tutorial: Render Quality (those damn pixels!)

Alrighty! I'm slowing down with my posts and to all who missed me, my apologies! ... I've had this Mandelbulb 3D tutorial in my head so I forgot a little that this is a blog and I can (and should) post about anything, in between tutorial pages :)

So I'll do that - but for now, I'm going to share with you my discovery of how to improve the state of your fractal if it's full of annoying little noisy pixels. As an example, I zoomed into an appropriate area using the Amazing Box formula, with lots of pixelation happening along the edges and in various spots, etc.

Now before I start, let me tell you this: The better you want your image to look like, the longer it will take to render. As I'm sure you already know, when you use the "preview" mode to render, it goes quickly, but the image is often riddled with pixels. As you go up in quality, using the "Video", "Mid" and "High" modes, renders take longer but the pixels start disappearing into nice smooth satisfying surfaces/curves.

(Something to note is that, sometimes (really, not always) a render with "High" mode comes out looking very different (and usually much better-looking) than in "Preview" mode. So do not give up after "Viewing to Main" once. Try Video and Mid, see if the fractal changes for the better, etc)

Something else very important to note is that often, as I'm sure you've already encountered, what you see in the Navigator window is not all what comes out in the Render window. This is just one of those things... Sometimes, it'll just be the colouring that's different, and sometimes, it's the whole shape of everything, as is the case with the example I used for this Tut page. In fact, let me start here. I said I used Amazing Box:

Zoom somewhere in Amazing Box in navigator window - 20 iterations

But then, when I clecked on view to main, and rendered the bugger in preview mode, I got this:

Mandelbulb 3D Tutorial: Cutting!

While playing around today on M3D, on a whim I decided to click on the Cutting tab in the Render window, just to have a look. 'Turns out, cutting can be a whole lot of fun :)

The Cutting Tab

To best demonstrate this great little tool, I'm going to use the same formula that loads on default when opening the program, except, I'm going to change the power and make it 2 instead of 8. Now many of you may have already loaded this formula with this little change, since the original 2D Mandelbrot set uses the 2nd power. And many of you would have gone, "Hmm, but that looks nothing even near the amazing Mandelbrot set!" ... Well, if you slice that weird looking thing using the cutting tool, you'll see something more familiar ;)

Allow me to demonstrate. Here is the very strange looking 3D version of the Mandelbrot set:

3D Mandelbrot Set

Next, I simply clicked on the z-axis checkbox (See image above), left the value as 0.00, and clicked Calculate 3D ... :

3D Mandelbrot Set cut along z Axis at 0.00

:) ... Remember this? Isn't it beautiful? Now, the nice thing about this is that, you can zoom into those little nooks and crannies, some of which are not really reachable when you're trying to navigate the entire 3D fractal in it's full bulk. Here, let me show you...:

Zoom-in 01

Zoom-in 02

Zoom-in 03

Nice :) Now let me change the colouring a bit so we can better see what's going on in there:

Well, it's only a little better, but you get the idea :) ... From here you can choose a spot, zoom in, zoom back out again, choose a different spot and try again, etc... With different formulas even the most experienced 3D fractalnauts would be able to find new and interesting areas had they never used cutting before.

Ok, now I'll load the original Mandelbulb (power 8) to demonstrate further. Here she is, cut in exactly the same way as above:

Mandelbulb cut along Z-axis at 0.00

Now, what happens if we change the value "0.00" ? It gets cut through either higher or lower, depending on, of course, whether you put in a positive or negative value. Here is a series of screenshots to demonstrate:

Mandelbulb cut along Z-axis at -0.8

Mandelbulb cut along Z-axis at -0.4

Mandelbulb cut along Z-axis at -0.2

Mandelbulb cut along Z-axis at 0.3

Mandelbulb cut along Z-axis at 0.6

So it follows that the same thing can be done with the x and y axis. And you can turn any/all of them on at the same time. Here I cut the Mandelbulb along the z and y axi, both at 0.00 (with a bit of rotation for a better view):

And that concludes my 5th Tutorial page about the wonderful Mandelbulb 3D program. Thanks for watching! :)


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: Render Quality

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