"Bald Eagle" <cre### [at] netscapenet> wrote:
>...
> Knowing partly what goes into all of this, I can see that it required a lot of
> time and attention to detail - and you always post fairly polished images, even
> if they are only WIPS.

Yes, it takes some time, but as long as it's interesting work I don't mind.

I seldom have time to polish finishes, textures or materials, so I mostly use
the default ones. But I do spend some time on the pigments and where to place
the light source and the camera.


> > I'm not very familier wit Paul Nylander's work. Those macros seem like a good
> > start for a library for complex calculations. But the Pow() macro could need
> > some work to allow for the exponent to also be a complex number.
>
> http://bugman123.com/index.html

Yes, I have seen his web pages some years ago, but I have never looked very
closely at them. They are quite "busy" with a layout that makes them a bit hard
to read - but they have many interesting topics. AFAIK he too lives in Norway.


> Complex exponents --- Oh, it makes my head hurt to even thing about that.

;-)

    A^B = e^ln(A^B) = e^(B*ln(A))

    pow(A, B) = exp(B*ln(A))

You already have formulas for complex exp() and multiplication - and
implementing ln() is not very hard.


> > I'm also wondering how hard it would be to use mod()
> > to have an infinite array of those "black hole vortices" on a plane - in either
> > a rectangular or an alternating/hexagonal arrangement...
>
> That's an interesting idea: to have a mod() operator that can handle complex
> values. But I don't know how to implement that...

Yes, that could be a way to create such repetitive patterns.

But it would be even better if a POV-Ray library could be made that can preserve
the repetitive nature of several of the complex operators (i.e. those that are
multi valued). I think that that would be quite hard to make...


> Maybe check out
> http://www.dimensions-math.org/Dim_E.htm
>
> and perhaps get in touch with the authors, since they seem to have an amazing
> grasp of both the math as well as POV-Ray.

That looks like an nice and interesting film. Thank you.


--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
>...
>
> I have now made a couple of rendering of this function with both the natural
> logarithm and the base 10 logarithm of the magnitude.
>
> It looks like your rendering was done with the base 10 logarithm. The attached
> rendering was done with the natural logarithm.
>
> It seems to me that using a logarithmic scale can sometimes reveal some extra
> information also in 3D.

Now my work with my POV-Ray library for complex functions has come a bit
further.

Here's an image where the domain colors for the function above are shown on a
plane. Here the lightness value for the colors are ramped up in intervals both
for the phase angle and the natural logarithm of the magnitude.

There are more images here for those that are interested:
https://github.com/t-o-k/POV-Ray-complex-functions

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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Attachments:
Download 'hueramps_magnramps.png' (493 KB)

Preview of image 'hueramps_magnramps.png'

Il 19/01/2022 17:22, Tor Olav Kristensen ha scritto:
 > "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
 > Here's an image where the domain colors for the function above are 
shown on a
 > plane. Here the lightness value for the colors are ramped up in 
intervals both
 > for the phase angle and the natural logarithm of the magnitude.
 >
 > There are more images here for those that are interested:
 > https://github.com/t-o-k/POV-Ray-complex-functions
 >
 > --
 > Tor Olav
 > http://subcube.com
 > https://github.com/t-o-k


This image is just beautiful!

Paolo

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Paolo Gibellini <p.g### [at] gmailcom> wrote:
> Il 19/01/2022 17:22, Tor Olav Kristensen ha scritto:
>  > "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
>  >...
>
> This image is just beautiful!

Thank you very much Paolo!

I was a bit worried that it might be only me that liked it.

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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Op 22/01/2022 om 04:25 schreef Tor Olav Kristensen:
> Paolo Gibellini <p.g### [at] gmailcom> wrote:
>> Il 19/01/2022 17:22, Tor Olav Kristensen ha scritto:
>>   > "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
>>   >...
>>
>> This image is just beautiful!
> 
> Thank you very much Paolo!
> 
> I was a bit worried that it might be only me that liked it.
> 
<grin> no.

-- 
Thomas

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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
>
> Here's an image where the domain colors for the function above are shown on a
> plane. Here the lightness value for the colors are ramped up in intervals both
> for the phase angle and the natural logarithm of the magnitude.

This image reminds me of turbofan jet engine fan blades.

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On 22/01/2022 04:25, Tor Olav Kristensen wrote:
> Paolo Gibellini <p.g### [at] gmailcom> wrote:
>> Il 19/01/2022 17:22, Tor Olav Kristensen ha scritto:
>>  > "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
>>  >...
>>
>> This image is just beautiful!
> 
> Thank you very much Paolo!
> 
> I was a bit worried that it might be only me that liked it.

No, no... me too of course;)
Very good job.

I don't have too much time right now, but I'm continuing my research.



-- 
Kurtz le pirate
Compagnie de la Banquise

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Attachments:
Download 'complex_frameworke_fn009.jpg' (100 KB)

Preview of image 'complex_frameworke_fn009.jpg'

Thomas de Groot <tho### [at] degrootorg> wrote:
> Op 22/01/2022 om 04:25 schreef Tor Olav Kristensen:
> > Paolo Gibellini <p.g### [at] gmailcom> wrote:
> >> Il 19/01/2022 17:22, Tor Olav Kristensen ha scritto:
> >>   > "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> >>   >...
> >>
> >> This image is just beautiful!
> >
> > Thank you very much Paolo!
> >
> > I was a bit worried that it might be only me that liked it.
> >
> <grin> no.

Good   =))

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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kurtz le pirate <kur### [at] gmailcom> wrote:
> On 22/01/2022 04:25, Tor Olav Kristensen wrote:
> > Paolo Gibellini <p.g### [at] gmailcom> wrote:
> >> Il 19/01/2022 17:22, Tor Olav Kristensen ha scritto:
> >>  > "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> >>  >...
> >>
> >> This image is just beautiful!
> >
> > Thank you very much Paolo!
> >
> > I was a bit worried that it might be only me that liked it.
>
> No, no... me too of course;)
> Very good job.

Thank you Kurtz. I'm glad to hear that !


> I don't have too much time right now, but I'm continuing my research.

That's yet another function with nice domain colors. It seems that you have a
talent for finding such functions.

Are your functions related for some physics related project that you are working
on ?

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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"Cousin Ricky" <rickysttATyahooDOTcom> wrote:
> "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> >
> > Here's an image where the domain colors for the function above are shown on a
> > plane. Here the lightness value for the colors are ramped up in intervals both
> > for the phase angle and the natural logarithm of the magnitude.
>
> This image reminds me of turbofan jet engine fan blades.

When you mention it; yes I agree.

And that would be a nice and colorful engine  ;-)

--
Tor Olav
http://subcube.com
https://github.com/t-o-k

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