Does anyone know if 4d Mandelbrots are possible as I've never seen any.

I'd also like to know if it's possible to make smooth mandelbrot 'mountains'
without height fields.  Mandelbrots always have these sharp edges between
levels.

--
/* Nekar Xenos */#local N=<-20,40,100>;#local K=<20,-40,100>;#local R=seed(0);
blob{#while((K-N).x>0)#local X=N;#local N=N+<rand(R),rand(R),1>/3;#local N=(
vlength(N-K)<vlength(X-K)?N:2*X-N);sphere{<N.y,-N.x,N.z>,1,1 scale .02}sphere{N
,1,1 scale.02}sphere{<-N.x-40,N.y,N.z>1,1 scale.01}sphere{<N.x+40,-N.y,N.z>1,1
scale.01 }#end pigment{rgbt 1}interior{media{emission <2,4,5>*5}}hollow}

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On Tue, 29 May 2001 17:05:08 +0200, "Nekar Xenos"
<j-p### [at] citywalkcoza> wrote:

>Does anyone know if 4d Mandelbrots are possible as I've never seen any.

There's a unique julia set for each point in the complex plane. That
makes for a 4D julibrot. Of course, the only interesting part of the
complex plane is where the M-set is :)


Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] vipbg
TAG      e-mail : pet### [at] tagpovrayorg

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"Peter Popov" <pet### [at] vipbg> wrote in message
news:lke7htcil5esgmqj7irqblih72u7s5v87h@4ax.com...
> On Tue, 29 May 2001 17:05:08 +0200, "Nekar Xenos"
> <j-p### [at] citywalkcoza> wrote:
>
> >Does anyone know if 4d Mandelbrots are possible as I've never seen any.
>
> There's a unique julia set for each point in the complex plane. That
> makes for a 4D julibrot. Of course, the only interesting part of the
> complex plane is where the M-set is :)

I understand the basics of Mandelbrot and did  understand Julia sets (forgotten
partly but I know there' a Julia set for every point on a Mandelbrot ). But I
don't quite understand where all the info comes for the fourth dimension of the
4d Julia and what the difference is(if any) between a 4d Julia and 4d Julibrot.
Maybe if you could explain that a bit more in detail. Maybe the 4d julibrot is a
Julia set that uses Mandelbrot info for the forth dimension?

Regards

Nekar

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"Nekar Xenos" <j-p### [at] citywalkcoza> schrieb im Newsbeitrag
news:3b13b9bd@news.povray.org...
> I'd also like to know if it's possible to make smooth mandelbrot
'mountains'
> without height fields.  Mandelbrots always have these sharp edges between
> levels.

Use a fractal program that does more than 256 gray scales. Then do some
smoothing in a paint program and you have a perfect bitmap for smooth
heightfields.

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"Bonsai" <bon### [at] b0n541net> wrote in message news:3b14a6b0$1@news.povray.org...
> "Nekar Xenos" <j-p### [at] citywalkcoza> schrieb im Newsbeitrag
> news:3b13b9bd@news.povray.org...
> > I'd also like to know if it's possible to make smooth mandelbrot
> 'mountains'
> > without height fields.  Mandelbrots always have these sharp edges between
> > levels.
>
> Use a fractal program that does more than 256 gray scales. Then do some
> smoothing in a paint program

That can be a bit tricky to prevent loosing detail where it is needed. What I'm
thinking of is if heightfields would only notice the edges of different colours
or grey scales and then with a spline or bezier algorithm fil in the space
inbetween \. resulting in something that is nicely scaleable.

Nekar

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Nekar Xenos <j-p### [at] citywalkcoza> wrote:
: I understand the basics of Mandelbrot and did  understand Julia sets (forgotten
: partly but I know there' a Julia set for every point on a Mandelbrot ).

  Not exactly. "There's a Julia set for each complex number" is the correct
terminology.

: But I
: don't quite understand where all the info comes for the fourth dimension of the
: 4d Julia

  The regular Julia set uses complex numbers, which are numbers with two
components. That is, it is a set of complex numbers.
  A 4D Julia set uses either quaternion of hypercomplex numbers. These are
numbers with four components.
  The formula is the same as with the regular Julia, but using quaternion
or hypercomplex numbers. The difference between these two is how their
product is calculated (the product of two numbers is well defined only
up to complex numbers but not to numbers with higher dimensions).

-- 
#macro N(D,I)#if(I<6)cylinder{M()#local D[I]=div(D[I],104);M().5,2pigment{
rgb M()}}N(D,(D[I]>99?I:I+1))#end#end#macro M()<mod(D[I],13)-6,mod(div(D[I
],13),8)-3,10>#end blob{N(array[6]{11117333955,
7382340,3358,3900569407,970,4254934330},0)}//                     - Warp -

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