There are two ways to calculate it in programming language:
- with Cartesian coordinates (real and imaginary part)
- with polar coordinates (radius and angle)
With both systems you can calculate the square of a value easily with real
values.

But what would happen, if we add a 3rd dimension?
Then you take spherical coordinates. For calculating the square you just
square the radius and double the 2 angles. You do the same thing to
calculate an apple man.

I have made some test scenes with POV-Ray, but it was very slow. I switched
to Visual Basic .NET and made an include-file. Every Point consists of 12
triangles, because meshes are faster than boxes.
The problem is: it takes too long to calculate a good image. My pictures are
full of pixels and unclear, but you can see that it is a fractal.

Maybe there are better ways to calculate such figures much more faster and
better. I think of something like isosurfaces. There's also the rule: draw
the point or not.

Clearly the x-y-plane shows an apple man, but not the two other planes.
interesting...

Did anyone heard about such an idea? Google couldn't find something.

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nomail@nomail wrote:
> Every Point consists of 12 triangles, because meshes are faster than boxes.

  *Ahem*

  If you render 1 mesh and then render 1 box, the box will probably
render faster.
  Thus if you create and render 1000 meshes and then create and render
1000 boxes, the boxes will probably still render faster.
  Also, the meshes will probably consume much more memory than the boxes.

  The difference may kick in if you create 1 mesh containing all the
triangles of the original 1000 meshes and compare that 1 mesh with
the 1000 boxes.

  So you shouldn't simply assume "meshes render faster than boxes". This
is true only in certain contexts.

  How are you creating the meshes? Have you actually compared the rendering
speed if you created boxes?

> Maybe there are better ways to calculate such figures much more faster and
> better. I think of something like isosurfaces. There's also the rule: draw
> the point or not.

  Mandelbrot-type fractals are often ugly and not very descriptive if you
render only the points inside the fractal.
  The most beautiful and descriptive Mandelbrot images are those where
the coloration of space depends on the number of iterations it took to
bail out. (It's descriptive because the color will tell you how close
that point is to the border of the fractal.)

  Of course this is easy to do in a 2D image, but not in a 3D image.

  You could do what the 4D Julia fractal does: Use a low iteration
amount and just render the surface of that iteration.

-- 
plane{-x+y,-1pigment{bozo color_map{[0rgb x][1rgb x+y]}turbulence 1}}
sphere{0,2pigment{rgbt 1}interior{media{emission 1density{spherical
density_map{[0rgb 0][.5rgb<1,.5>][1rgb 1]}turbulence.9}}}scale
<1,1,3>hollow}text{ttf"timrom""Warp".1,0translate<-1,-.1,2>}//  - Warp -

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>   If you render 1 mesh and then render 1 box, the box will probably
> render faster.
>   Thus if you create and render 1000 meshes and then create and render
> 1000 boxes, the boxes will probably still render faster.
>   Also, the meshes will probably consume much more memory than the boxes.
>
>   The difference may kick in if you create 1 mesh containing all the
> triangles of the original 1000 meshes and compare that 1 mesh with
> the 1000 boxes.

Of course I made one mesh containing all these triangles. They were in most
cases faster. But the main reason was, that with a mesh i didn't need 4 GB
RAM.

>   So you shouldn't simply assume "meshes render faster than boxes". This
> is true only in certain contexts.
>
>   How are you creating the meshes? Have you actually compared the rendering
> speed if you created boxes?

Every box consists of 12 triangles. I create the edge-point with VB and
include the triangle-file in POV-Ray

> > Maybe there are better ways to calculate such figures much more faster and
> > better. I think of something like isosurfaces. There's also the rule: draw
> > the point or not.
>
>   Mandelbrot-type fractals are often ugly and not very descriptive if you
> render only the points inside the fractal.
>   The most beautiful and descriptive Mandelbrot images are those where
> the coloration of space depends on the number of iterations it took to
> bail out. (It's descriptive because the color will tell you how close
> that point is to the border of the fractal.)
>
>   Of course this is easy to do in a 2D image, but not in a 3D image.
>
>   You could do what the 4D Julia fractal does: Use a low iteration
> amount and just render the surface of that iteration.

That's what I also thought of. Only rendering the points of one plane
crossing the figure. Then it is possible to color. hmmm...
I'will try it, when I have enough time, not yet. Maybe next week-end.

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nomail@nomail nous apporta ses lumieres ainsi en ce 15/06/2004 03:27... :

>
>Every box consists of 12 triangles. I create the edge-point with VB and
>include the triangle-file in POV-Ray
>
>  
>
Since when POV Ray break up boxes into triangles? Using: box{1,-1} only 
generate 1 item, using zero triangle.

Alain

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Alain <aze### [at] qwertygov> wrote:
> >Every box consists of 12 triangles. I create the edge-point with VB and
> >include the triangle-file in POV-Ray

> Since when POV Ray break up boxes into triangles? Using: box{1,-1} only 
> generate 1 item, using zero triangle.

  He did not mean that POV-Ray generates triangles from a box.

-- 
#macro N(D)#if(D>99)cylinder{M()#local D=div(D,104);M().5,2pigment{rgb M()}}
N(D)#end#end#macro M()<mod(D,13)-6mod(div(D,13)8)-3,10>#end blob{
N(11117333955)N(4254934330)N(3900569407)N(7382340)N(3358)N(970)}//  - Warp -

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