I was bored, and the recursive torii post got me thinking of recursion, 
so I made a simple macro that draws the Sierpinski Pyramid.  Before I 
made this, I didn't know POV-Ray allowed macros to call themselves. 
This particular image is built from 78,125 pyramids, each made using 6 
triangles, for a total of 468,750 triangles, all wrapped up in a single 
mesh with some radiosity, sky_sphere, and a plane tacked on.

(NOTE: I did some searching around...some places show the Sierpinski 
Pyramid as having 3 sides on the base, others with 4.  4 was easier to 
implement, so I used that.)

-DJ

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Attachments:
Download 'sierpinksi.png' (239 KB)

Preview of image 'sierpinksi.png'

When you use a four-sided base, it makes the base (and all the mini-bases)
solid - this makes the structure look heavier/thicker - so there's some
artistic considerations to be made.
Recursive works for this - but random-walk is, IMHO, more fun ;)

Anyway, tasty stuff.

-s
5TF!

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If you manage to make things like this when you're bored, I wonder what 
creations you do if you are fully in rendering..?

Best greetings,

Sven

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DJ Wiza <Kil### [at] sohcahtoanet> wrote:
> I was bored, and the recursive torii post got me thinking of recursion,
> so I made a simple macro that draws the Sierpinski Pyramid.

Recursion is fun! Here's a similar pyramid in the Menger-Sierpinski family I
did late last year.

// Persistence Of Vision raytracer version 3.5 sample file.
//
// -F -A0.4 +AM2 +R1
// -D +A0.1 +AM2 +R4
// -d +A0.05 +AM2 +R3
//
// Auth: PM 2Ring
//

global_settings {
  assumed_gamma 1
  //max_trace_level 10
  #if(0)
  radiosity {
    pretrace_end 0.08
    always_sample off
  }
  ambient_light 0
  #end
}

#include "textures.inc"

#declare RoomRad = 30;
#declare Do_Room = 1;

#declare Eye=<0, 5.0,-11>/sqrt(410)*RoomRad *.55;

camera {
  location  Eye
  right x*image_width/image_height up y
  direction z
  angle 40

  look_at   1.65*y
}

//light_source {Eye + <1,1,1> * .05 rgb .4}
light_source {<-7, 15, -12>/sqrt(113)*RoomRad * .7 rgb 1}

//---Textures------------------------------------------------------------------

#declare FMetal =
finish {
  ambient 0.02
  diffuse 0.35  *2
  //phong 0.65 phong_size 120
  specular .5 roughness 1e-4
  //brilliance 3

  //metallic
  //reflection {0.75 metallic}
  reflection {0.2}
}

#declare FShiny =
finish {
  ambient 0.05 diffuse 0.75
  specular .25 roughness 1e-4
  //brilliance .5
  reflection 0.175
}

#declare Checker =
texture{
  pigment { checker rgb 1 transmit 1, rgb 0.05 transmit .25 rotate 45*y
scale 4 }
  finish {FShiny}
}

//---Objects------------------------------------------------------------------

#declare RR = sqrt(.5);

#macro RBox(A,W,C,D)
  sphere{A, W*RR pigment{colour C}finish{FMetal}}
  //box{A, A+W pigment{colour C}finish{FMetal}}
  //box{A, A+W material{M_NB_Glass texture{pigment{colour C filter 1}}}}
  #if(D>0)
    #local WW=W/2;
    #local DD=D-1;
    RBox(A+x*W,WW, (C+x)/2,DD)
    RBox(A+y*W,WW, (C+y)/2,DD)
    RBox(A+z*W,WW, (C+z)/2,DD)
  #end
#end

#declare RCrystal =
union {
  RBox(0, 2, rgb 1, 5)

  rotate <0, -225, 0>
  translate z*sqrt(2)
}

//The room
#declare Room =
union{
  sphere{
    0, RoomRad
    pigment {
      //rgb .55
      gradient y
      color_map {
        [0 rgb <0, 0, .1>]
        [1 rgb <.1,.2,1>*2]
      }
      scale RoomRad/2
    }

    finish{ambient .1 diffuse .5}
    //normal{granite .1 scale .02}
  }
  #if(1)
  box{
    <-1, -1/RoomRad, -1>, <1, 0, 1> scale RoomRad

    //texture{White_Marble scale 2}texture{Checker}
    pigment{crackle solid} normal{crackle 1} finish{FShiny}
  }
  #end

  hollow
  no_shadow

  translate -2*y
}

//---The
scene------------------------------------------------------------------

object{RCrystal}

#if(Do_Room)
  object{Room}
#else
  background {rgb .5}
#end

//---------------------------------------------------------------------

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Attachments:
Download 'rblockb2.jpg' (135 KB)

Preview of image 'rblockb2.jpg'