Hi people,

after some playing around with simple puppets (see all those "pigs" here and
in p.b.i. ) I revisited the realm of fractals. Here the Sierpinsky triangle
is rotating through disconnected stages into something vaguely resembling a
snowflake - though NOT Koch's snowflake, obviously. I don't know what the
final fractal is called - searching the net for "Sierpinsky" gives too many
hits :-)

I apologize for the quality - fractals don't compress so well ...

comments welcome (or else I woudn't post it here)

Karl

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Attachments:
Download 'sierpins.mpg' (593 KB)

> Hi people,
> 
> after some playing around with simple puppets (see all those "pigs" here and
> in p.b.i. ) I revisited the realm of fractals. Here the Sierpinsky triangle
> is rotating through disconnected stages into something vaguely resembling a
> snowflake - though NOT Koch's snowflake, obviously. I don't know what the
> final fractal is called - searching the net for "Sierpinsky" gives too many
> hits :-)
> 
> I apologize for the quality - fractals don't compress so well ...
> 
> comments welcome (or else I woudn't post it here)
> 
> Karl

Nice ! But really too short or too quick: one has barely the time to see 
what happens. Can you make a slower version ?


tuabiht

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Thibaut Jonckheere <tua### [at] MAPSONyahoofr> wrote:
>
> Nice ! But really too short or too quick: one has barely the time to see
> what happens. Can you make a slower version ?
>
>
> tuabiht

Hello Thibaut,
Thank you. My main interest in this thing is the final shape. Since this
thing parses awfully slowly on my old Mac (about two minutes per frame) and
I would like go back to different things in my sparse spare time, I propose
you do that for yourself. Since the source is quite short, I hope it will
be ok  if I append it here:

//----- cut here for sierpinsky.pov

//#include "VectorStuff.inc"
#include "transforms.inc"

#macro UnitV_XY( Phi ) // from my VectorStuff.inc; UnitVector in xy-plane
   < cos( radians( Phi ) ), sin( radians( Phi ) ), 0  >
#end //#macro UnitV_XY( phi )

#declare TransForms = array[3] ;

#declare cc = 0;
#while( cc < 3 )
 #declare TransForms[cc] =
 transform{
  scale 0.5
  rotate 60*clock*z
// angles outside 0..60 give same pictures, partially mirrored
  translate UnitV_XY( cc*120-30 )
 }
 #declare cc = cc+1;
#end // #while( cc < 3 )

#declare ptnum = 20000; // more would be better, but traces SLOWLY
#declare skip = 10;
#declare ptnum = ptnum+skip;
#declare Points = array[ptnum];

#declare MyStream = seed( 0 );

#declare cc = 0;
#declare Points[cc] = < 0,0,0 >;
#declare Points[cc] = < 2*rand(MyStream)-1, 2*rand(MyStream)-1, 0 >;

#while( cc < skip-1 )
   #declare cc = cc+1;
   #declare Points[cc] =
      vtransform( Points[cc-1], TransForms[3*rand(MyStream)] );
#end //#while( cc < skip-1 )

#while( cc < ptnum-1 )
   #declare cc = cc+1;
   #declare Points[cc] =
      vtransform( Points[cc-1], TransForms[3*rand(MyStream)] );
   sphere{ Points[cc]+4*z 0.005 pigment{ color 0 } }
#end //#while( cc < ptnum-1 )

camera {
 up y right x*image_width/image_height
}

background{ color 1 }

//----- end of sierpinsky.pov

some comments:
- "ptnum" gives the number of spheres finally traced; 20000 is MINIMUM !
- render with square picture and lowest quality settings; the spheres are
used as pixels, no reflections or shading required
- make an animation; clock going from 0...1 as usual, with as many pictures
as you want (or care to watch tracing)

This is just a quick hack, you probably don't need to put all the points
into an array, but I'm not going to work on it for the time being because
of other projects I'm dreaming of ...

Thank you for your comments

Karl

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> Thank you. My main interest in this thing is the final shape. Since this
> thing parses awfully slowly on my old Mac (about two minutes per frame) and
> I would like go back to different things in my sparse spare time, I propose
> you do that for yourself. Since the source is quite short, I hope it will

ok, I' ll dot it. With a recent machine, parse/render is not really a 
problem (for me, with ptnum=100000, parse time is 32 sec. and render 
time is 5 sec. at 800x800)

I will post the animation as soon as possible


Thibaut

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Thibaut Jonckheere <tua### [at] MAPSONyahoofr> wrote:
> ok, I' ll dot it. With a recent machine, parse/render is not really a
> problem (for me, with ptnum=100000, parse time is 32 sec. and render
> time is 5 sec. at 800x800)
>
> I will post the animation as soon as possible
>
>
> Thibaut

Sounds like a plan :-)
I have about 30 secs parse time with ptnum=5000 (five thousand), so you may
understand why I don't want to detail that any further. There is always the
possibility of rendering over night, of course ...

I'm looking forward to a refined version of this.

Greetings
Karl

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> Thibaut Jonckheere <tua### [at] MAPSONyahoofr> wrote:
>> ok, I' ll dot it. With a recent machine, parse/render is not really a
>> problem (for me, with ptnum=100000, parse time is 32 sec. and render
>> time is 5 sec. at 800x800)
>>
>> I will post the animation as soon as possible
>>
>

The anim should now be visible at :
http://big.chez-alice.fr/tuabiht/sierpinski01.gif

(animated gif, size ~ 1.8 Mo)

To see more clearly the inital and final states, I have put small pauses 
at these points.


tuabiht

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Thibaut Jonckheere <tua### [at] MAPSONyahoofr> wrote:
>
> The anim should now be visible at :
> http://big.chez-alice.fr/tuabiht/sierpinski01.gif
>
> (animated gif, size ~ 1.8 Mo)
>
> To see more clearly the inital and final states, I have put small pauses
> at these points.
>
>
> tuabiht

Looks great - and BIG :-)
Thank you for your efforts and your cpu time.
I am still searching for the name of the snowflake-like thingie which is
(not quite) in the middle of your animation and at the end of mine. I can't
imagine that something so regular has not been found before. Until now I
have not found another picture of it on the net, but the search continues
....

Greetings
Karl

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> Looks great - and BIG :-)
> Thank you for your efforts and your cpu time.

You are welcome. This was very little work in fact (the most difficult 
bit was to put it on the internet :-).

My next plan, which will require more work, is to read and understand 
your code !

Thibaut

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Thibaut Jonckheere <tua### [at] MAPSONyahoofr> wrote:
>
> My next plan, which will require more work, is to read and understand
> your code !
>

Hi Thibaut,

I COULD go into lengthy explanations here, but RealLife(TM) is interfering
in form of my little daughter (aged 6), who has caught quite a cold!
But here are some keywords for mathematical background:
"iterated function systems" and "chaos game"; you might have a look at
http://mathworld.wolfram.com/ for some (very short) explanations.

Greetings

Karl

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Thibaut Jonckheere <tua### [at] MAPSONyahoofr> wrote:

> My next plan, which will require more work, is to read and understand
> your code !
>
> Thibaut

Some people who are interested in Sierpinsky fractals also use Fractint. :-)

http://spanky.triumf.ca/www/fractint/fractint.html


Stephen

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