Navigating 3D-space (Mandelbulb3D - first steps)

8 min read

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Sabine62's avatar
By Sabine62
Fractal Art


Mandelbulb3D is a fractal generating program that aims at creating 3D-fractals that are often quite realistic looking.

2D-fractal software like Jux can only create fractals that are flat
, while 3D-fractals also have height/depth (and of course there are the in-betweens: some programs like UltraFractal are mainly 2D, but have (very limited) 3D-possibilities). The best comparison might be a photograph (which is always 2D) you had printed from some shells. For instance, you can see the shells but if you let your hand touch the photo, it feels like a flat surface. If 3D-photos would exist, you would be feeling the shells sticking out of the flat surface.

Clipboard01 by Sabine62


Most mandelbulb3D-users navigate through their fractal by using the Navigation window. You will find it on the upper left of the main window by clicking the 3D Navi-button


But what really happens when we move around in our fractal in the navigation window? In there we can move our fractal in a 2D-way (up and down, left and right, rotate, as you could do with a photo), but also in a 3D-way (back and front, but also rotating a shape around you as if you'd stand in the middle). This is good to know and realize when trying to find your bearings even in complex fractals.

Mandelbulb3Dv18{
g.....S....O/...1.........E3aPbYgEXwzmQZAlZ1.R5ECEyU3xGLZzXhpmX7jJrEzMyyvt8m.T/E
................................VBwofIK4Wz1........A./..................y.2...wD
...Uz6...El/.....M.1/.....kO1...8.....E4.....UlT9fV2O.sD/..........m/dkpXm1....U
z.EnAnQD12../..........wz.................................U0.....y1...sD...../..
.z1...kDANPQN6V4.y1..........agK1HQaVdejBiVspm6bJr9Hq4L4Gc/Uz2ZoA8QaVdejG7BX0bNM
eu1nOBAlN4aey2MvLUV2O.sDU.....I1..............sD.6....sD..G.....................
.............oAnAt1...sD....zw1........................................./....k1.
.....Ksulz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.26nzzXCc..kYEkti4xyD6s41pmERLz1...........k.5xzFrA0.
.U.Ehl2Ilz1.GZwV7TN..1...........6.LyP/4g............s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveemKN94.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv...U.06fee0U.0MQIJ3U.06Ewy5U.06f................................
E....2..F2E.....I....w.....Jj7LRnVIHKxKOY/UQ.........................6U./2E./2E.
GMU/46E./.......................................................OaNaNaNadznAnAnA
nAnozcNaNaNaNauD........kz1........................................wz...........
........kz1.............}
{Titel: donut}

Paste these parameters into your program so we can have a look.
This is what you get to see when you calculate.

Clipboard03 by Sabine62


Let's have a look at the navigation window:

Clipboard04 by Sabine62

Make sure all checks and numbers circled in red are set the same as above. If you miss the right and/or lower part of the menu, please click the arrows to open them.

In the image above you see the axes in the centre along which the donut shape is placed. If we move it to the left of right, we move it along the red X-axis, if we move it up or down, we move it a long the green Y-axis, and if we move it to the back or front (and this is what 3D is all about really), we move it along the blue Z-axis.

Maybe the best way to understand what you are looking at here is imagining that you are looking into some kind of box with flexible walls with in it a floating donut.

Clipboard05 by Sabine62Clipboard06 by Sabine62
Donut model by montcalm 3dwarehouse.sketchup.com/model…

You can walk into the box and get closer to the donut, or you walk backwards creating more distance to the donut. This not the same as zooming in. Zooming only enlarges the image you are looking at as if you were using a magnifying glass, while when you choose Walking in the navigation window you actually get closer to the donut.

You can test this by clicking repeatedly on Zoom. As you can see you are getting closer and closer and closer to the surface until it vanishes. Of course if you now set the Far Plane on the lower left to 5000, the surface will be visible again, but if you keep clicking Zoom, it will vanish again.

Click on the button
Parameter to load the original again from the main window. You saw that zooming does work just like a magnifier on a photo: everything appears bigger, but the photo is not moved towards you nor are you moved towards the photo.

Now click twice on the upper
Walking -button and you'll see this:


Clipboard07 by Sabine62


Walking does actually move you towards or back from (with the lower button) the donut, and it can do what zooming cannot: It can actually enter the shape. This is what we have done here, and to our surprise the donut appears to be hollow! The green inner circle is the actual inside of the donut, the grey surfaces are the places where the solid outlines have been cut through (it is possible to render also the cut outlines: on the formula tab on the lower right where it says now Outside render choose in and outside).

And if we walk even further, we must end up with the donut behind us. Let's try that: click on Walking 6 times. The image appears to be empty. In the real we would now turn around 180 degrees to see our donut again. In the navigation window you can do that with
Looking. Click on the right of left arrow button above Looking and keep clicking until you see the donut again (under Looking you can see the Looking + Rolling angle, which is set to 10, so you'll have to click 18 (18 x 10 degrees=180 degrees) times until you have the donut opposite to you again). Notice the difference with moving to the left or right with the Sliding arrow-buttons. If you click those, the donut just moves to the left or the right, only when you use the Looking you turn to look for the donut. Experiment with walking towards and back from the donut and notice how the angles of the coords *(coordinates) change with every click. Of course, walking into structures does work with every shape, not just donuts;)

Click on
Parameter to reload the original image.

The same as
Looking to the left or right happens when you use the up or down buttons of Looking: You turn to look. Try it and see how the donut-shape changes because the angle under which we see it changes. Whereas if you take the Sliding up or down button, you only move the shape up or down. Experiment with both to see the difference and remember that you can always click Parameter to reload the original fractal.

Simply put you could say that Zoom and Sliding are 2D operations (as is Rolling, which basically only rotates the whole image you see, not the shape), while Walking and Looking are 3D-operations.

For some inspiration on what you can achieve when you have a good understanding of navigating in 3D, have a look at these animations

by nic022 

Scarabaeus Prime by EricTonArts by EricTonArts 

And a much less sophisticated but more lightweight one by me FWQ3D: Asurf (again III) by Sabine62 in case your computer has trouble loading the ones above
Comments40
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Thank you so much, building tutorials are a lot of work. So I appreciate what you have done. Lesson 1 done.

Fractalpilot's avatar

5th time thru all Hals Tutorials again :)

One these days I'll stick...

On The bright side I can do The Resistance in My sleep now!

Lior-Art's avatar
Excellent explanations :hug:
Sabine62's avatar
I am glad you find them helpful:) :hug:
Lior-Art's avatar
I worked with Vue Infinite but I was understanding those x,y,z
But with MDB3D I really didn't understand how it  works
Even if I changed one of x or y or z it didn't make any change in the POV even if I was rendering but  no change.
Now with your explanation  I know the direction I want to take.
I've understood this thanks to your explanations.
:hug:
Sabine62's avatar
I am so glad, Lior! :) :hug:
nic022's avatar
Cool, thank you a lot for the mention. Your explanation are clear and it is a good idea to writte this journal.

:)
Sabine62's avatar
Most welcome, Nic, your art is a great inspiration!
zisgul's avatar
wat ben ik blij met deze uitleg , maar het moet ff wachten, krijg de 24 de sleutel , dus het is nu de reorganiseren , wegdoen naar kringloop of stortHug 
Sabine62's avatar
Ohh jeeeee... Ik wens je heel veel succes en sterkte ook, verhuizen is leuk maar ook mega-zwaar met alle gesjouw en geregel en geklus! Heb je wel genoeg hulp?
Weggooien/wegdoen/weggeven is goed voor de ziel, denk ik altijd, een soort van opruimen in jezelf, overbodige ballast kwijtraken;)
zisgul's avatar
Dat is het zeker ,maar reuze vermoeiend!
HairBrainedScenes's avatar
Awesome Feature article Sabine
Sabine62's avatar
Thank you very much, Ken! :)
HairBrainedScenes's avatar
Very Welcome Sabine Meow :3 
Undead-Academy's avatar
Cool one dear friend :)
Sabine62's avatar
Thank you so very much , dear!:)
Undead-Academy's avatar
always with great pleasure dear friend :)
AnnaKirsten's avatar
What a wonderful tut on use of those basic buttons!!  I do have one question:  In Walking, we have (w) at the top and (s) at the bottom.  It might be obvious, but I've not worked out what the w and s actually stand for?  (Always thought it was wide or shallow...)
HalTenny's avatar
Those are the keyboard shortcut keys. (They don't stand for anything) You can use the keyboard with the associated keys instead of mouse clicking the buttons. It's much faster once you get used to it. :)
AnnaKirsten's avatar
Oh I see!  Thanks so much for that info! :)
Sabine62's avatar
Thank you very much, Anna, I am glad you find it useful :) and thank you, HalTenny, for clearing that one up:)
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