Logo by kameelian - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Visit the official fractalforums.com Youtube Channel
 
Home Help Search Gallery Downloads Login Register
*
Welcome, Guest. Please login or register. October 03, 2018, 01:00:29 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Welcome to Fractal Forums > Fractal Software > 3D Fractal Generation > What's the volume of the Mandelbox?
Pages: [1]   Go Down
« previous next »
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: What's the volume of the Mandelbox?  (Read 893 times)
0 Members and 1 Guest are viewing this topic.
greentexas
Navigator
*****
Posts: 64
« on: November 09, 2016, 12:07:28 AM »
Could someone figure out the volume of the Mandelbox? It could be that the volume of this fractal is zero (like the Menger sponge), and I've seen the Mandelbox emptying.
Logged
Tglad
Fractal Molossus
**
Posts: 703


WWW
« Reply #1 on: November 10, 2016, 05:45:59 AM »
I think it is zero (i.e. its fractal dimension is less than 3)... however I don't have proof and it seems to get denser as you get towards the centre. So there might be a depth at which no points can escape.
Logged
KRAFTWERK
Global Moderator
Fractal Senior
******
Posts: 1439


Virtual Surreality


WWW
« Reply #2 on: November 10, 2016, 07:49:10 PM »
Not bad to get an answer from Mr. Mandelbox himself.
And I love the end of the answer "So there might be a depth at which no points can escape."
Sounds like a poetic description of a black hole...  afro
Logged
Surreal Fractals http://mandelwerk.deviantart.com/
3Dprinted Fractals https://www.shapeways.com/shops/mandelpieces
Buddhi
Fractal Iambus
***
Posts: 895



WWW
« Reply #3 on: November 10, 2016, 10:08:27 PM »
Here is some kind of experiment to support Tglad's answer. When maximum number of iterations is very high then Mandelbox starts to be empty. Theoretically when maxiter will be infinite number, then Mandelbox will disappear.

Mandelbox was rendered here as a cross section at z = 0
Logged
My fractal gallery: http://krzysztofmarczak.deviantart.com
fractal animations: http://www.youtube.com/user/xlace
Mandelbulber program: https://github.com/buddhi1980/mandelbulber2
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it
« Reply #4 on: November 10, 2016, 10:40:19 PM »
Nice idea Buddhi but I think it is not a way to demonstrate that fact, who knows if it is due to an artefact of the distance estimation?
The topic is very interesting of course smiley
Logged
No sweat, guardian of wisdom!
Tglad
Fractal Molossus
**
Posts: 703


WWW
« Reply #5 on: November 11, 2016, 01:25:54 AM »
Great images. Josleys also talked about the Mandelbox disappearing for higher iterations (http://images.math.cnrs.fr/Mandelbox.html?lang=fr)

My thought on this is that having zero volume (or D<3) does not necessarily mean that the object should be invisible. A plane has zero volume and is visible, and any 'shell' fractal is still visible:

and 'foam' fractals are still visible:


For certain angles at least, it looks like Menger sponge and maybe even 3D cantor dust would be visible... I give an example here  http://www.fractalforums.com/3d-fractal-generation/the-mandelbox-is-tenuous/msg15558/#msg15558.


For fractals that definitely are ultimately invisible (their 2D screen projection has fractal dimension < 2), such as trees, an interesting topic is that there are different ways to render it that keep it visible without it being an approximation http://tglad.blogspot.com.au/2012/12/dimension-aware-rasterising.html (I even made a paper on it 'Improving image clarity using local feature dimension'), but it has never been attempted in 3D.
« Last Edit: November 11, 2016, 01:50:50 AM by Tglad » Logged
Buddhi
Fractal Iambus
***
Posts: 895



WWW
« Reply #6 on: November 11, 2016, 07:24:59 AM »
You are right about disappearing. The fractal will be still visible but all remaining surfaces will have zero thickness. That's why they disappear when is used used raymarching with bisection algorithm.
Logged
My fractal gallery: http://krzysztofmarczak.deviantart.com
fractal animations: http://www.youtube.com/user/xlace
Mandelbulber program: https://github.com/buddhi1980/mandelbulber2
woronoi
Alien
***
Posts: 32
« Reply #7 on: November 11, 2016, 07:33:54 AM »
Cantor dust. That was a great answer for me.
Logged
gurroa
Forums Freshman
**
Posts: 11
« Reply #8 on: November 11, 2016, 10:52:45 AM »
I am counting virtual size of 3D fractals from the lowest possible rendered resolution.

Program FractaloScop can get to 0.0000001.
If we imagine this structural resolution as a 1 cm, 1.0 represents 100km, 2PI's MandelBulb is virtualy a 628km wide ball.
If we imagine it instead as a 0.1 mm, 1.0 still represents 1km and MandelBulb shrinks to a 6.28km ball.
And so on...

The same logic can be applied to MandelBox too, but there is a catch.
MandelBox can be easily resized and so heavily vary in size.
I have changed almost each line of equation (just to get more readable inner space) and the default size for my program is now set to 12.
So the mandelbox for me is a virtual box sized 1200km when the smallest geometry detail rendered as a pixelized block is a 1cm.

Maybe you can use the same logic to count virtual volume too.

This video is showing what I mean by "unreadable inner space" in almost :-) default MandelBox.
I have called it the Abstract shortcut.
<a href="https://www.youtube.com/v/60SQel4zsr0&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/60SQel4zsr0&rel=1&fs=1&hd=1</a>

After my changes the current inner space become more like this at only really few iterations.
<a href="https://www.youtube.com/v/NWM15uJYI9A&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/NWM15uJYI9A&rel=1&fs=1&hd=1</a>
Logged
Pages: [1]   Go Down
« previous next »
  Print  
« previous next »
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
New Volume Render 3D Fractal Generation doncasteel8587 2 1582 Last post November 12, 2006, 08:08:07 PM
by Nahee_Enterprises
another volume renderer 3D Fractal Generation lycium 1 1184 Last post August 01, 2007, 10:20:43 PM
by Nahee_Enterprises
volume rendering with ImageVis3D General Discussion « 1 2 » makc 19 2991 Last post March 31, 2010, 11:58:11 AM
by makc
Volume Shaders Mandelbulber atmycrossroads 0 1383 Last post May 07, 2012, 04:02:40 PM
by atmycrossroads
Fractal Building Code + Volume 4 Movies Showcase (Rate My Movie) Brummbaer 1 495 Last post May 16, 2013, 06:20:55 PM
by Dinkydau

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.14 seconds with 26 queries. (Pretty URLs adds 0.013s, 2q)