Hi folks,

I recently came across Paul Nylander's website at http://www.bugman123.com.
Marvellous images of 3D fractals rendered with Mathematica.
Exceptional rendering times and amazing images!
He also published some code to render Mandelbulbs in Povray.

Here is SDL for one of the Mandelbulbs:

// Mandelbulb - power 4 - Believe me the power 6 is a vision of hell!

// Adapted from original function for power 8 by Paul Nylander at
http://www.bugman123.com;
// Trace time on an AMD Ryzen7 Eight Core using 16 threads: 7 h 54 min with
max_gradient 1000
// Trace time on an AMD Ryzen7 Eight Core using 16 threads: 2 h 34 min with
max_gradient 200
-------------------------------------------------------
#version 3.7;
global_settings { assumed_gamma 2.2 }

// #include "colors.inc"
// #include "textures.inc"
// #include "math.inc"

camera{
 location <1.75,4,-5.5>
 look_at <0.0, 0.0, 0.0>
 up y
 sky y
 angle 25
}


light_source{<-20.00, 30.00, -20.00> color rgb < 1.0, 0.498039, 0.0 >} // color
Coral
light_source{<20.00, -30.00, 0.00> color rgb < 0.847059, 0.847059, 0.74902 >} //
color Wheat

#declare n=4;

#declare f=function(i,x,y,z,xc,yc,zc) {select(i>0 & x*x+y*y+z*z<4, 0,
sqrt(x*x+y*y+z*z),

f(i-1,pow(x*x+y*y+z*z,n/2)*cos(n*atan2(y,x))*cos(n*atan2(z,sqrt(x*x+y*y)))+xc,
        pow(x*x+y*y+z*z,n/2)*sin(n*atan2(y,x))*cos(n*atan2(z,sqrt(x*x+y*y)))+yc,
        -pow(x*x+y*y+z*z,n/2)*sin(n*atan2(z,sqrt(x*x+y*y)))+zc,xc,yc,zc))};

isosurface{
 function{f(24,0,0,0,x,y,z)}
 threshold 2
 max_gradient 200 // found by Povray: 33566
 contained_by{sphere{0,1.5}}
 pigment{rgb 1}
}
//end
----------------------------------------------------------------
But a word of warning before you start:
DO NOT ACTIVATE any INC-FILE! When I did Povray crashes as soon as I start
rendering!

Has anyone an idea why Povray crashes?

There is only a warning in the Message Window that says something like
'iterations are not allowed in this function'.

Happy tracing - and when you do: grab a big snack and a big mug of coffee before
you do!

Droj

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Attachments:
Download 'mandelbulb_power4.png' (1117 KB)

Preview of image 'mandelbulb_power4.png'

On 07/05/2024 23:41, Droj wrote:
> 
> // Adapted from original function for power 8 by Paul Nylander at
> http://www.bugman123.com;
> // Trace time on an AMD Ryzen7 Eight Core using 16 threads: 7 h 54 min with
> max_gradient 1000
> // Trace time on an AMD Ryzen7 Eight Core using 16 threads: 2 h 34 min with
> max_gradient 200
> -------------------------------------------------------

Hi, Droj !

Very interesting - thanks for sharing.
I've rendered this 800x600 image with max_gradient=1000 (No other
parameters was changed) on Intel(R) Xeon(R) CPU E5-2690 v2 @ 3.00GHz
(40 cores) for 2 min 19 sec and can't figure out how to get make it more
detailed.

Any suggestions, please !
--
YB

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Attachments:
Download 'fract_01.png' (288 KB)

Preview of image 'fract_01.png'

On 07/05/2024 23:41, Droj wrote:
> 
> // Adapted from original function for power 8 by Paul Nylander at
> http://www.bugman123.com;
> // Trace time on an AMD Ryzen7 Eight Core using 16 threads: 7 h 54 min with
> max_gradient 1000
> // Trace time on an AMD Ryzen7 Eight Core using 16 threads: 2 h 34 min with
> max_gradient 200
> -------------------------------------------------------

Hi, Droj !

Very interesting - thanks for sharing.
I've rendered this 800x600 image with max_gradient=1000 (No other
parameters was changed) on Intel(R) Xeon(R) CPU E5-2690 v2 @ 3.00GHz
(40 cores) for 2 min 19 sec and can't figure out how to make it more
detailed.

Any suggestions, please !
-- 
YB

Post a reply to this message

Attachments:
Download 'fract_01.png' (288 KB)

Preview of image 'fract_01.png'

On 07/05/2024 23:41, Droj wrote:
> // Mandelbulb - power 4 - Believe me the power 6 is a vision of hell!

Agree with you - sometimes it looks horrible ...
--------------------------------------------------------------------
camera{location <-2.5,5,5> look_at <-0.5,0,0.3> up z sky z angle 25}
light_source{20*z,1}

#declare f=function(i,x,y,z,xc,yc,zc) {select(i>0 & x*x+y*y+z*z<4, 0, 
sqrt(x*x+y*y+z*z), 
f(i-1,(x*x-y*y)*(1-z*z/(x*x+y*y))+xc,2*x*y*(1-z*z/(x*x+y*y))+yc,-2*z*sqrt(x*x+y*y)+zc,xc,yc,zc))};

isosurface{function{f(24,x,y,z,x,y,z)} threshold 0.5 max_gradient 1000 
contained_by{sphere{<-0.5,0,0>,2}} pigment{rgb 1}}
--------------------------------------------------------------------

--
YB.

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Attachments:
Download 'fract_02.png' (163 KB) Download 'fract_02_1.png' (117 KB)

Preview of image 'fract_02.png'

Preview of image 'fract_02_1.png'

yesbird <sya### [at] gmailcom> wrote:

>
> Very interesting - thanks for sharing.
> I've rendered this 800x600 image with max_gradient=1000 (No other
> parameters was changed) on Intel(R) Xeon(R) CPU E5-2690 v2 @ 3.00GHz
> (40 cores) for 2 min 19 sec and can't figure out how to get make it more
> detailed.
>
> Any suggestions, please !
> --
> YB

Hi yesbird

as I can see you have no problem with the rendering time as I have.

You can increase max_gradient.
When I rendered it the max_gradient Povray found was 33566.

So give it a go.

Droj

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On 09/05/2024 16:23, Droj wrote:
> So give it a go.

Hi, Droj.

Thank you, I will try.
--
YB

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On 09/05/2024 16:23, Droj wrote:
> When I rendered it the max_gradient Povray found was 33566.

It took 15m59,185s for rendering with max_gradient=33566, and n=6,
but I see, that your image looks more smooth and pretty.
What's the secret ? Antialiasing, maybe ... Could you please post
all rendering parameters ?

> // Mandelbulb - power 4 - Believe me the power 6 is a vision of hell!

This teddy bear don't looks like real daemon, but some sort of inferno
is present, no doubt ...
--
YB

Post a reply to this message

Attachments:
Download 'mand_pow_6_1600x1200.png' (1117 KB)

Preview of image 'mand_pow_6_1600x1200.png'

yesbird <sya### [at] gmailcom> wrote:

> It took 15m59,185s for rendering with max_gradient=33566, and n=6,
> but I see, that your image looks more smooth and pretty.
> What's the secret ? Antialiasing, maybe ... Could you please post
> all rendering parameters ?

Hi YB
Oh man you make me weep! 16 min with max_gradient=33566 ... if I try my image
will be finished next week.
Here are the settings of the ini-file I use:
-----------------
Width = 1600
Height = 1200
Antialias = On
Sampling_Method = 1
Antialias_Threshold = 0.0010
Jitter = Off
Antialias_Depth = 9
Output_To_File = On
Output_File_Type = N
Display = On
Verbose = Off
Quality = 11
Input_File_Name =
Output_File_Name =
Initial_Frame = 0
Final_Frame = 0
Subset_Start_Frame = 0
Subset_End_Frame = 0
Test_Abort = On
Test_Abort_Count = 100
--------------------------
>
> > // Mandelbulb - power 4 - Believe me the power 6 is a vision of hell!
>
> This teddy bear don't looks like real daemon, but some sort of inferno
> is present, no doubt ...

Have you ever seen Edvard Munk's painting 'The Scream'? It's disturbing but
Mandelbulb power 6 is worse.

Hope the ini settings will help.

Droj

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On 10/05/2024 01:04, Droj wrote:> Oh man you make me weep! 16 min with 
max_gradient=33566 ... if I try my image
> will be finished next week.
Hi, Droj.

Please, don't cry: I noticed, that your setting are too 'aggressive':
; Antialias_Depth = 9
; Antialias_Threshold = 0.0010
See: https://www.povray.org/documentation/view/3.6.1/223/

making less depth and threshold can seriously improve performance with
almost the same quality.

> Hope the ini settings will help.
Thanks for setting, you've saved a lot of time for me.

> Have you ever seen Edvard Munk's painting 'The Scream'?Yes, sure, this is a famous
painting, but I see something close to
Francisco Goya. :)

Happy poving,
--
YB

Post a reply to this message

Attachments:
Download 'fract_03_800x600.png' (95 KB)

Preview of image 'fract_03_800x600.png'

On 10/05/2024 01:04, Droj wrote:
>> Oh man you make me weep! 16 min with max_gradient=33566 ...

Hi, Droj.

Please, don't cry: I noticed, that your setting are too 'aggressive':
; Antialias_Depth = 9
; Antialias_Threshold = 0.0010
See: https://www.povray.org/documentation/view/3.6.1/223/

making less depth and threshold can seriously improve performance with
almost the same quality.

>> Hope the ini settings will help.

Thanks for setting, you've saved a lot of time for me.

>> Have you ever seen Edvard Munk's painting 'The Scream'?

Yes, sure, this is a famous painting, but I see something close to
Francisco Goya. 🙂

Happy poving,
-- 
YB

Post a reply to this message

Attachments:
Download 'fract_03_800x600.png' (95 KB)

Preview of image 'fract_03_800x600.png'

On 10/05/2024 01:04, Droj wrote:
> Oh man you make me weep! 16 min with max_gradient=33566 ...

Hi, Droj.

Please, don't cry: I noticed, that your setting are too 'aggressive':
; Antialias_Depth = 9
; Antialias_Threshold = 0.0010
See: https://www.povray.org/documentation/view/3.6.1/223/

making less depth and threshold can seriously improve performance with
almost the same quality.

>  Hope the ini settings will help.

Thanks, you've saved a lot of time for me.

> Have you ever seen Edvard Munk's painting 'The Scream'?Yes, sure, this is a famous
painting, but I see something close to
Francisco Goya. 🙂

Happy poving,
-- 
YB

Post a reply to this message

Attachments:
Download 'fract_03_1024x768.png' (192 KB)

Preview of image 'fract_03_1024x768.png'

On 10/05/2024 01:04, Droj wrote:
> Oh man you make me weep! 16 min with max_gradient=33566 ...
Hi, Droj.

Please, don't cry: I noticed, that your setting are too 'aggressive':
; Antialias_Depth = 9
; Antialias_Threshold = 0.0010
See: https://www.povray.org/documentation/view/3.6.1/223/

making less depth and threshold can seriously improve performance with
almost the same quality.

>   Hope the ini settings will help.
Thanks, you've saved a lot of time for me.

>  Have you ever seen Edvard Munk's painting 'The Scream'?

Yes, sure, this is a famous painting, but I see something close to
Francisco Goya. 🙂

Happy poving,
-- 
YB

Post a reply to this message

Attachments:
Download 'fract_03_1024x768.png' (192 KB)

Preview of image 'fract_03_1024x768.png'

yesbird <sya### [at] gmailcom> wrote:

Hi YB

> Please, don't cry: I noticed, that your setting are too 'aggressive':
> ; Antialias_Depth = 9
> ; Antialias_Threshold = 0.0010
> See: https://www.povray.org/documentation/view/3.6.1/223/
>
> making less depth and threshold can seriously improve performance with
> almost the same quality.

Yes, you are right. I will lower the aa and see what happens.

>
> >  Have you ever seen Edvard Munk's painting 'The Scream'?
>
> Yes, sure, this is a famous painting, but I see something close to
> Francisco Goya. 🙂
>

Yeah, Francisco Goya would have been my next choice.

Could you please share the code for your fractal03.png? It's amazing!

And do you have an idea how to code power 3, power 5 and power 7?

Happy tracing
Droj

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On 10/05/2024 15:06, Droj wrote:
> Could you please share the code for your fractal03.png? It's amazing!
With pleasure - see attachment :).

> And do you have an idea how to code power 3, power 5 and power 7?
Did not thought about it, but if you have some cool ideas, please feel
free to send me scenes and I will render them on my fast server.

PS:I am mostly working at the night and sometimes afraid to open newly
rendered fractal image, feeling like opening door to inferno :).

All the best,
--
YB

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Attachments:
Download 'fractals.pov.txt' (3 KB) Download 'povray.ini.txt' (3 KB)

yesbird <sya### [at] gmailcom> wrote:

Hi YB

> With pleasure - see attachment :).
thank you for sharing.
I realised that your camera position is on positive z-axis while mine is on
negative z-axis. That explains why some of your images look different.

I also took your advice and changed my 'aggressive' aa settings - and yes,
rendering times decreased a lot. Thanks for putting me on the right track.

>
> > And do you have an idea how to code power 3, power 5 and power 7?
>
Yes, see attachment - 3 fractal beasts - well, I am not too happy with it as the
fractals look a bit 'truncated'. I can't perform any experiments with the code
like use larger contained_by values. Maybe, you can with your excellent server!

>
> PS:I am mostly working at the night and sometimes afraid to open newly
> rendered fractal image, feeling like opening door to inferno :).
>
Same here: Seeing the image slowly evolving at night is somtimes like watching
the movie 'Hellraiser' :))

Happy tracing
Droj
PS: Did you try to rotate any of the fractals? I would like to know your
experience.

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Attachments:
Download 'mandelbulb_pow3_5_7.pov.txt' (3 KB)

On 11/05/2024 22:27, Droj wrote:

Hi, Droj.

> Thanks for putting me on the right track.
Always welcome :).

> Yes, see attachment - 3 fractal beasts - well, I am not too happy with it as the
> fractals look a bit 'truncated'. I can't perform any experiments with the code
> like use larger contained_by values. Maybe, you can with your excellent server!
I've played width them a little, results in attachments. I like 'pow3'
most of all. To make them more smooth and less boring I changed
threshold and increased AA.

> PS: Did you try to rotate any of the fractals? I would like to know your
> experience.

No, but idea is interesting - will try soon. Also, I guess, threshold
animation can give interesting results (two 640x480 attached), need to
try it too, when I will have a break in my present project.

If you have another set of beasts, I can also render them with pleasure.
Good luck with explorations,
--
YB.

Post a reply to this message

Attachments:
Download 'mandelbulb_pow3_5_7_mod_pow3_tr1.8.png' (291 KB) Download 'mandelbulb_pow3_5_7_mod_pow5_tr2.png' (330 KB) Download 'mandelbulb_pow3_5_7_mod_pow7_tr1.png' (325 KB) Download 'mandelbulb_pow3_5_7_mod_pow7_tr2.png' (117 KB) Download 'mandelbulb_pow3_5_7_mod_pow7_tr05.png' (145 KB) Download 'mandelbulb_pow3_5_7_mod.pov.txt' (3 KB) Download 'povray.ini.txt' (3 KB)

Preview of image 'mandelbulb_pow3_5_7_mod_pow3_tr1.8.png'

Preview of image 'mandelbulb_pow3_5_7_mod_pow5_tr2.png'

Preview of image 'mandelbulb_pow3_5_7_mod_pow7_tr1.png'

Preview of image 'mandelbulb_pow3_5_7_mod_pow7_tr2.png'

Preview of image 'mandelbulb_pow3_5_7_mod_pow7_tr05.png'

You guys may want to check out Inigo Quilez's page, and look at the "Fractals &
complex dynamics" section.

https://iquilezles.org/articles/

Articles:
Continuous iteration count
The M1 bulb of the Mandelbrot set
The M2 bulb in the Mandelbrot set
Area of M1 in the Mandelbrot set
The symmetry of the Mandelbrot set
Introduction to the Mandelbrot set

They might offer some insights into how to speed up your renders.

- BW

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hi,

"Droj" <803### [at] drojde> wrote:
> ...
> // Mandelbulb - power 4 - Believe me the power 6 is a vision of hell!

a less "hellish" bulb, derived from the work of Chris M. Thomasson.

mp4, approx 12M: <https://photos.app.goo.gl/Us3fXASWaMPWDEhc9>


regards, jr.

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"jr" <cre### [at] gmailcom> wrote:
> hi,
>
> "Droj" <803### [at] drojde> wrote:
> > ...
> > // Mandelbulb - power 4 - Believe me the power 6 is a vision of hell!
>
> a less "hellish" bulb, derived from the work of Chris M. Thomasson.
>
> mp4, approx 12M: <https://photos.app.goo.gl/Us3fXASWaMPWDEhc9>
>
>
> regards, jr.

Hi jr,

thanks for the link.
Looks like 'The Ghost in the Bottle' ;)

regards, Droj

Post a reply to this message

"Bald Eagle" <cre### [at] netscapenet> wrote:
> You guys may want to check out Inigo Quilez's page, and look at the "Fractals &
> complex dynamics" section.
>
> https://iquilezles.org/articles/
>
> Articles:
> Continuous iteration count
> The M1 bulb of the Mandelbrot set
> The M2 bulb in the Mandelbrot set
> Area of M1 in the Mandelbrot set
> The symmetry of the Mandelbrot set
> Introduction to the Mandelbrot set
>
> They might offer some insights into how to speed up your renders.
>
> - BW

Hi Bill,

thank you for the link to Inigo's website.
I read some of his articles and understood - zilch.

The problem I had with these Mandelbulbs was that - what Paul Nylander called
'inefficient code' - it gave Povray a really hard time.

And when I added an include file Povray crashes as soon as I started rendering.

Well, I guess I put that Mandelbulb topic on ice until I have a more powerful
computer.

Regards, Droj

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hi,

"Droj" <803### [at] drojde> wrote:
> ...
> Looks like 'The Ghost in the Bottle' ;)

[OT] an idle search on this found <https://www.youtube.com/watch?v=jt-hkyxDJQg>.
 :-)


regards, jr.

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