Logo by Fiery - 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: Did you know ? you can use LaTex inside Postings on fractalforums.com!
 
*
Welcome, Guest. Please login or register. January 22, 2018, 11:15:02 AM


Login with username, password and session length


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


Pages: 1 ... 25 26 [27] 28 29 ... 37   Go Down
  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: True 3D mandelbrot type fractal  (Read 383197 times)
0 Members and 2 Guests are viewing this topic.
xenodreambuie
Conqueror
*******
Posts: 124



WWW
« Reply #390 on: November 09, 2009, 12:01:00 PM »

Hi Jos,
I like the quality that your DE formula produces. The problem you have may be due to using z1=R.sin(ph), which only gives one hemisphere. Changing it to z1= -R.sin(ph) is necessary to flip the orbits between hemispheres.
Logged

Regards, Garth
http://xenodream.com
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #391 on: November 09, 2009, 12:20:17 PM »

I don't get the holes Jos is getting even using positive sine - this is the closest I got to getting such holes (a much deeper zoom):



Here's virtually the same area using negative sine:

Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
JosLeys
Strange Attractor
***
Posts: 258


WWW
« Reply #392 on: November 09, 2009, 12:59:00 PM »

Well, I used the formula quoted in the article, which has z=R.cos(ph) !

And yes, Dave, I am limiting the max step to not be greater than the smallest observed for a particular iter count, but in a simpler way than what you sent me. I'll look at that again.
I'm sure I have a bug somewhere...thanks, I'll keep searching.
Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #393 on: November 09, 2009, 01:14:44 PM »

Hi Daniel, it appears that you've quoted a different formula to the ones we've been using ?

For Paul's version of your formula I'm sure he quoted it as:

              r = magn^@mpwr
              dth = @mpwr*(th = atan2(zri))
              dph = @mpwr*(ph = asin(zj/magn))
              zri = r*(cos(dth)*cos(dph) + flip(cos(dph)*sin(dth))) + cri
              zj = -r*sin(dph) + cj

Then I also had two versions suggested by Garth:

              r = (magn=sqrt(magn))^@mpwr
              th = @mpwr*atan2(zri)
              ph = @mpwr*acos(zj/magn)
              zri = r*(cos(th)*sin(ph) + flip(sin(ph)*sin(th))) + cri
              zj = r*cos(ph) + cj

              r = magn^@mpwr
              dth = @mpwr*(th = atan2(zri))
              if (ph = acos(zj/magn))>0.5*#pi
                ph = #pi - ph
              endif
              dph = @mpwr*ph
              zri = r*(cos(dth)*sin(dph) + flip(sin(dph)*sin(dth))) + cri
              zj = r*cos(dph) + cj


I'm guessing but what Jos has rendered may well be correct for the formula you quoted in your article - I'm just about to try it....
« Last Edit: November 09, 2009, 01:16:29 PM by David Makin » Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #394 on: November 09, 2009, 01:35:40 PM »

Hi Daniel, it appears that you've quoted a different formula to the ones we've been using ?

For Paul's version of your formula I'm sure he quoted it as:

              r = magn^@mpwr
              dth = @mpwr*(th = atan2(zri))
              dph = @mpwr*(ph = asin(zj/magn))
              zri = r*(cos(dth)*cos(dph) + flip(cos(dph)*sin(dth))) + cri
              zj = -r*sin(dph) + cj

Then I also had two versions suggested by Garth:

              r = (magn=sqrt(magn))^@mpwr
              th = @mpwr*atan2(zri)
              ph = @mpwr*acos(zj/magn)
              zri = r*(cos(th)*sin(ph) + flip(sin(ph)*sin(th))) + cri
              zj = r*cos(ph) + cj

              r = magn^@mpwr
              dth = @mpwr*(th = atan2(zri))
              if (ph = acos(zj/magn))>0.5*#pi
                ph = #pi - ph
              endif
              dph = @mpwr*ph
              zri = r*(cos(dth)*sin(dph) + flip(sin(dph)*sin(dth))) + cri
              zj = r*cos(dph) + cj


I'm guessing but what Jos has rendered may well be correct for the formula you quoted in your article - I'm just about to try it....


Apologies - I forgot, Paul essentially quoted ph = @mpwr*(atan(zj/cabs(zri)) - using the above was suggested by Garth as a faster alternative. Also don't worry about the dph/ph in the first version, I quoted from part of my code using Jos' analytical DE which requires the ph value multplied by (@mpwr-1).
« Last Edit: November 09, 2009, 01:38:39 PM by David Makin » Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #395 on: November 09, 2009, 02:06:42 PM »

Sorry - I missed Paul's recent post where he quotes the triplex formula he's using - that's the formula I'm using too.

Jos I'd be interested to know exactly what your formula was that was producing the "holes" since it's quite different from what I get from any versions of the formula - I also tried the formula that Daniel has quoted in his article (were ph and th are reversed etc.) but still didn't get a result with holes like yours.
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
JosLeys
Strange Attractor
***
Posts: 258


WWW
« Reply #396 on: November 09, 2009, 03:10:44 PM »

Quote
Jos I'd be interested to know exactly what your formula was that was producing the "holes" since it's quite different from what I get from any versions of the formula

OK, here it is : (the first part handles what is needed for the derivative)
   dzx= @pow*(R^(@pow-1))*Rdz*sin(phdz+(@pow-1)*ph)*cos(thdz+(@pow-1)*th)+c
   dzy= @pow*(R^(@pow-1))*Rdz*sin(phdz+(@pow-1)*ph)*sin(thdz+(@pow-1)*th)
   dzz= @pow*(R^(@pow-1))*Rdz*cos(phdz+(@pow-1)*ph)
     Rdz=sqrt(dzx*dzx+dzy*dzy+dzz*dzz)
     thdz=atan2(dzx+i*dzy)
     phdz=acos(dzz/Rdz)

   zx= (R^@pow)*sin(@pow*ph)*cos(@pow*th)+cx
   zy= (R^@pow)*sin(@pow*ph)*sin(@pow*th)+cy
   zz=(R^@pow)*cos(@pow*ph)+cz
     R=sqrt(zx*zx+zy*zy+zz*zz)
     th=atan2(zx+i*zy)
     ph=atan2(sqrt(zx*zx+zy*zy)+i*zz)

..but remember, as I said, it could still well be a weird rendering error
Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #397 on: November 09, 2009, 04:57:18 PM »

Quote
Jos I'd be interested to know exactly what your formula was that was producing the "holes" since it's quite different from what I get from any versions of the formula

OK, here it is : (the first part handles what is needed for the derivative)
   dzx= @pow*(R^(@pow-1))*Rdz*sin(phdz+(@pow-1)*ph)*cos(thdz+(@pow-1)*th)+c
   dzy= @pow*(R^(@pow-1))*Rdz*sin(phdz+(@pow-1)*ph)*sin(thdz+(@pow-1)*th)
   dzz= @pow*(R^(@pow-1))*Rdz*cos(phdz+(@pow-1)*ph)
     Rdz=sqrt(dzx*dzx+dzy*dzy+dzz*dzz)
     thdz=atan2(dzx+i*dzy)
     phdz=acos(dzz/Rdz)

   zx= (R^@pow)*sin(@pow*ph)*cos(@pow*th)+cx
   zy= (R^@pow)*sin(@pow*ph)*sin(@pow*th)+cy
   zz=(R^@pow)*cos(@pow*ph)+cz
     R=sqrt(zx*zx+zy*zy+zz*zz)
     th=atan2(zx+i*zy)
     ph=atan2(sqrt(zx*zx+zy*zy)+i*zz)

..but remember, as I said, it could still well be a weird rendering error

Hi, in Daniel's article he actually put:

------------------------
r = sqrt(x^2 + y^2 + z^2 )
theta = atan2(sqrt(x^2 + y^2) , z)
phi = atan2(y,x) ;

newx = r^n * sin(theta*n) * cos(phi*n)
newy = r^n * sin(theta*n) * sin(phi*n)
newz = r^n * cos(theta*n)
------------------------

I presume for phi he meant atan(y/x) or atan2(x+flip(y)).

Here's what I used based on Daniel's above version:

              dr = @mpwr*(r=sqrt(|dzri|+sqr(dzj)))*(magn=sqrt(magn))^(@mpwr-1.0)
              dph = (@mpwr-1.0)*ph + atan2(dzri)
              dth = (@mpwr-1.0)*th + asin(dzj/r)
              dzri = dr*(cos(dph)*sin(dth) + flip(sin(dth)*sin(dph)))
              dzj = dr*cos(dth)
              if @fractaltype==1 ; 1==Mandy
                dzri = dzri + 1.0
              endif
              r = magn^@mpwr
              dph = @mpwr*(ph = atan2(zri))
              dth = @mpwr*(th = asin(zj/magn))
              zri = r*(sin(dth)*cos(dph) + flip(sin(dth)*sin(dph))) + cri
              zj = r*cos(dth) + cj
              magn = |zri| + sqr(zj)

You should note that for my version magn, ph and th are precalculated before entry into the iteration loop.
It turns out that z^2+c for the above gives a 180 degree rotation of Garth Thornton's suggested formula (the "correct" one) but is quite different from Garth's at higher powers.
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
JosLeys
Strange Attractor
***
Posts: 258


WWW
« Reply #398 on: November 09, 2009, 05:21:47 PM »

Well , I see
Quote
theta = atan2(sqrt(x^2 + y^2) , z)

Sorry, my mistake then. In my code I'm actually using pi/2-theta by mistake.
Let's see if that makes my "tunnels" go away...
Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #399 on: November 09, 2009, 05:28:47 PM »

Quote
Jos I'd be interested to know exactly what your formula was that was producing the "holes" since it's quite different from what I get from any versions of the formula

OK, here it is : (the first part handles what is needed for the derivative)
   dzx= @pow*(R^(@pow-1))*Rdz*sin(phdz+(@pow-1)*ph)*cos(thdz+(@pow-1)*th)+c
   dzy= @pow*(R^(@pow-1))*Rdz*sin(phdz+(@pow-1)*ph)*sin(thdz+(@pow-1)*th)
   dzz= @pow*(R^(@pow-1))*Rdz*cos(phdz+(@pow-1)*ph)
     Rdz=sqrt(dzx*dzx+dzy*dzy+dzz*dzz)
     thdz=atan2(dzx+i*dzy)
     phdz=acos(dzz/Rdz)

   zx= (R^@pow)*sin(@pow*ph)*cos(@pow*th)+cx
   zy= (R^@pow)*sin(@pow*ph)*sin(@pow*th)+cy
   zz=(R^@pow)*cos(@pow*ph)+cz
     R=sqrt(zx*zx+zy*zy+zz*zz)
     th=atan2(zx+i*zy)
     ph=atan2(sqrt(zx*zx+zy*zy)+i*zz)

..but remember, as I said, it could still well be a weird rendering error

I should read code more carefully Jos - I just noticed you have:

     phdz=acos(dzz/Rdz)

but:

     ph=atan2(sqrt(zx*zx+zy*zy)+i*zz)
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
JosLeys
Strange Attractor
***
Posts: 258


WWW
« Reply #400 on: November 09, 2009, 05:41:08 PM »

Well it seems I was using the complement of the angle by mistake.
The 'holes' are now plugged.
Sorry for the wild goose chase


* 4D_test_88cbis.jpg (159.5 KB, 640x640 - viewed 1246 times.)
Logged
bugman
Conqueror
*******
Posts: 122



WWW
« Reply #401 on: November 09, 2009, 05:57:57 PM »

I would really like to ask xenodreambuie, how did you find the roots for the -2 power triplex? Do you have a means of finding the roots for arbitrary powers, and if so, how do you verify root validity?

I tried to create a 3D Glynn set using MIIM, but no luck so far. I also found that my MIIM code did nothing to improve my 4th order inverse 3D Julia set. On the up side, I was able to reproduce some similar images to xenodreambuie's 3D Julia sets using the MIIM code.

What does "flip" mean in UltraFractal code?
« Last Edit: November 09, 2009, 06:13:40 PM by bugman » Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #402 on: November 09, 2009, 06:00:12 PM »

Well it seems I was using the complement of the angle by mistake.
The 'holes' are now plugged.
Sorry for the wild goose chase


No problem - it helped because I just noticed the obvious with respect to my version of the analytical DE and changed it so that ph and th do not need precalculatiing - it just needed their calculation moving to the start of the iteration loop !
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #403 on: November 09, 2009, 06:02:32 PM »

(like "flip" for example).


Hi Paul

flip(f)

is just i*f

smiley

Edit: Aargh - make that flip(x+i*y) is (y+i*x) !
« Last Edit: October 01, 2011, 06:46:44 AM by David Makin » Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
JosLeys
Strange Attractor
***
Posts: 258


WWW
« Reply #404 on: November 09, 2009, 08:44:16 PM »

Now that I know that my distance estimate formula works better than I thought, I tried a really deep zoom.
The image below has magnification 28.8 million, and the surface treshold is 10^-12. If I haven't made a mistake, this means that if the total object is the size of the earth, then we are looking at an area the size of a dining table.

I think this about as deep as I can go with current state of the code.


* 4D_test_89l.jpg (179.62 KB, 640x640 - viewed 1551 times.)
Logged
Pages: 1 ... 25 26 [27] 28 29 ... 37   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Implementation: 3D mandelbrot type fractal 3D Fractal Generation « 1 2 » steamraven 27 23151 Last post August 21, 2016, 12:13:13 AM
by ironfractal
Re: True 3D mandelbrot type fractal Other / General Discussion shanest 2 10747 Last post November 20, 2009, 03:24:26 AM
by fractalrebel
True 3D mandelbrot fractal (search for the holy grail continues) The 3D Mandelbulb « 1 2 ... 17 18 » illi 260 49452 Last post November 25, 2010, 12:57:55 AM
by cKleinhuis
New fractal type... latest 3d type.. a z^2 for Benoit Images Showcase (Rate My Fractal) M Benesi 0 3015 Last post October 21, 2010, 07:14:00 AM
by M Benesi
My First Mandelbrot...Okay not true. Images Showcase (Rate My Fractal) Zephitmaal 3 2378 Last post January 07, 2012, 04:30:36 PM
by Pauldelbrot

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 0.416 seconds with 27 queries. (Pretty URLs adds 0.017s, 2q)