Logo by Trifox - 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 01, 2018, 06:37:10 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 > Mandelbox with "smooth" conditions
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: Mandelbox with "smooth" conditions  (Read 2075 times)
0 Members and 1 Guest are viewing this topic.
Buddhi
Fractal Iambus
***
Posts: 895



WWW
« on: April 19, 2011, 08:44:49 PM »
I'm not sure whether somebody tried this before, but I converted standard Mandelbox formula into formula without any conditions but with smooth transition functions.

I have replaced condition IF A>B by
\frac{1}{1 - \frac{1}{exp(k * (A-B))}}

where k is a smoothness factor

The code for Mandelbox is following (tested in Mandelbulber):
Code:
double sm = 3.0;

double zk1 = 1.0 / (1.0 + 1.0 / exp(sm * (z.x - par.mandelbox.doubles.foldingLimit)));
double zk2 = 1.0 / (1.0 + 1.0 / exp(sm * (z.x + par.mandelbox.doubles.foldingLimit)));
z.x = z.x * (1.0 - zk1) + (par.mandelbox.doubles.foldingValue - z.x) * zk1;
z.x = z.x * (zk2) + (-par.mandelbox.doubles.foldingValue - z.x) * (1.0 - zk2);

double zk3 = 1.0 / (1.0 + 1.0 / exp(sm * (z.y - par.mandelbox.doubles.foldingLimit)));
double zk4 = 1.0 / (1.0 + 1.0 / exp(sm * (z.y + par.mandelbox.doubles.foldingLimit)));
z.y = z.y * (1.0 - zk3) + (par.mandelbox.doubles.foldingValue - z.y) * zk3;
z.y = z.y * (zk4) + (-par.mandelbox.doubles.foldingValue - z.y) * (1.0 - zk4);

double zk5 = 1.0 / (1.0 + 1.0 / exp(sm * (z.z - par.mandelbox.doubles.foldingLimit)));
double zk6 = 1.0 / (1.0 + 1.0 / exp(sm * (z.z + par.mandelbox.doubles.foldingLimit)));
z.z = z.z * (1.0 - zk5) + (par.mandelbox.doubles.foldingValue - z.z) * zk5;
z.z = z.z * (zk6) + (-par.mandelbox.doubles.foldingValue - z.z) * (1.0 - zk6);

r = z.Length();
double r2 = r * r;

double m_factor1 = fR2 / mR2;
double m_factor2 = fR2 / r2;
double rk1 = 1.0 - 1.0 / (1.0 + 1.0 / exp(sm * (r2 - mR2)));
double rk2 = 1.0 - 1.0 / (1.0 + 1.0 / exp(sm * (r2 - fR2)));
double rk21 = (1.0 - rk1) * rk2;

z = z * (1.0 - rk1) + z * (m_factor1 * rk1);
z = z * (1.0 - rk21) + z * (m_factor2 * rk21);

z = z * scale + constant;
r = z.Length();

As you see there is no any "IF" command.

Bellow there is an example:

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=6817

The shape is almost the same, but a little more rounded somewhere

This is other example:

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=6792

Of course rendering is much slower but shapes are very interesting somewhere
Logged
My fractal gallery: http://krzysztofmarczak.deviantart.com
fractal animations: http://www.youtube.com/user/xlace
Mandelbulber program: https://github.com/buddhi1980/mandelbulber2
marius
Fractal Lover
**
Posts: 206
« Reply #1 on: April 19, 2011, 09:08:47 PM »
Quote from: Buddhi on April 19, 2011, 08:44:49 PM
I'm not sure whether somebody tried this before, but I converted standard Mandelbox formula into formula without any conditions but with smooth transition functions.

I have replaced condition IF A>B by
<Quoted Image Removed>

where k is a smoothness factor

Interesting. More organic, H.R. Giger-style appearance.
Nice glow rendering!
Logged
msltoe
Iterator
*
Posts: 187
« Reply #2 on: April 20, 2011, 04:03:57 AM »
Buddhi,

 I've experimented with smooth transitions for my favorite YZ symmetrized Mandelbulbs, but found in those cases I had to use sharp functions to prevent artifacts.
 I've looked at and others have mentioned the use of sin(x) for reflections  but found that the sine function is too smooth.
 BTW, the formula in your post has a typo : it should read: 1/1+exp... but I see you coded it up correctly.

 If you want you can post the smooth and non-smooth side by side so we can see the difference. I've been concerned though, that any smooth transition actually causes conformality violations. In other words, the if-test formula, even though it's discontinous in first derivative, preserves angles as you zoom in.

-mike
Logged
Buddhi
Fractal Iambus
***
Posts: 895



WWW
« Reply #3 on: April 20, 2011, 07:15:46 AM »
Quote from: msltoe on April 20, 2011, 04:03:57 AM
Buddhi,

 I've experimented with smooth transitions for my favorite YZ symmetrized Mandelbulbs, but found in those cases I had to use sharp functions to prevent artifacts.
 I've looked at and others have mentioned the use of sin(x) for reflections  but found that the sine function is too smooth.
 BTW, the formula in your post has a typo : it should read: 1/1+exp... but I see you coded it up correctly.

 If you want you can post the smooth and non-smooth side by side so we can see the difference. I've been concerned though, that any smooth transition actually causes conformality violations. In other words, the if-test formula, even though it's discontinous in first derivative, preserves angles as you zoom in.

-mike

You are right, There was a mistake and I have also overcomplicated a little this formula. I forgot that exp(x) = 1/exp(-x)  embarrass It could be:
\frac{1}{1 + \frac{1}{exp(k * (A-B))}} = \frac{1}{1 + {exp(k * (B-A))}
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: April 21, 2011, 06:41:47 PM »
Quote from: msltoe on April 20, 2011, 04:03:57 AM
If you want you can post the smooth and non-smooth side by side so we can see the difference. I've been concerned though, that any smooth transition actually causes conformality violations.

Too bad it's true - I tried many times to write a smoothed Barnsley using sigmoids like these and they all give weird Julias due to the non conformality. sad
Logged
No sweat, guardian of wisdom!
knighty
Fractal Iambus
***
Posts: 819
« Reply #5 on: May 22, 2011, 03:02:08 PM »
Quote from: Buddhi on April 19, 2011, 08:44:49 PM
I'm not sure whether somebody tried this before, but I converted standard Mandelbox formula into formula without any conditions but with smooth transition functions.

I did  grin. But your results are much better.
There is also this one.
Logged
Pages: [1]   Go Down
« previous next »
  Print  
« previous next »
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
"Smooth" folding 3D Fractal Generation knighty 13 3721 Last post September 18, 2011, 12:23:53 PM
by DarkBeam
Special "offset" and "rotate" options from Fractallab possible in M3d-formula? Mandelbulb 3d « 1 2 » SaMMy 18 5182 Last post April 05, 2011, 12:20:52 PM
by DarkBeam
Rotated "Mandelbox surface" Amazing Box, Amazing Surf and variations Kali 0 854 Last post July 23, 2011, 06:58:51 PM
by Kali
A "smooth" transition ... Mandelbulb 3d « 1 2 » DarkBeam 19 1940 Last post September 28, 2011, 04:41:27 PM
by DarkBeam
"Futuristic City Under Construction" Mandelbox Flight Movies Showcase (Rate My Movie) mcsoftware 0 166 Last post February 03, 2016, 07:37:18 PM
by mcsoftware

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 0.164 seconds with 24 queries. (Pretty URLs adds 0.016s, 2q)