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superset Sierpinski gaskets--> between a gasket and a carpet

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  • Roger Bagula
    I got the 2d version of the beta Sierpinski cube working as an IFS. and it s version where the start points are zero instead of a square. 8 points taken as 12
    Message 1 of 1 , May 1, 2004
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      I got the 2d version of the beta Sierpinski cube working as an
      IFS. and it's version where the start points are zero instead of a square.
      8 points taken as 12 points but sequentially with 1/3 probability each
      (Sierpinski gasket supersets?)
      These are all combinatorial and BAM ( binary address Method)
      types I've gotten before, but never got them working as IFS before.
      It's possible to define an ifs cube with eight corners and four
      transforms each now.
      The pictures as well as the 3d version is at:
      http://photos.groups.yahoo.com/group/caostheory/lst?.dir=/3d+fractals&.src=gr&.order=&.view=t&.done=http%3a//briefcase.yahoo.com/
      My dxf of the Mathematica 3d Beta Sierpinski cube has been used in art at:

      > Caplyn Dor- Surreal FantasyScapes and Geometrics


      http://users.adelphia.net/~cdorsurreal/cdorpage1.html
      <http://users.adelphia.net/%7Ecdorsurreal/cdorpage1.html>
      True basic program:
      PRINT "input Sierpinski number 3 to 12"
      LET m=3
      LET n0=4
      SET MODE "color"
      SET WINDOW 0,1920,0,1024
      SET COLOR MIX (1) 0,0, 0
      SET BACKGROUND COLOR "white"
      LET x=1
      LET y=1
      LET c=0
      LET s1=400
      LET s2 =(s1)*1024/1920
      DIM a(25,5),b(25,5),e(25,5),f(25,5)
      LET a(1,1)=-1
      LET b(1,1)=-1
      LET a(2,1)=0
      LET b(2,1)=-1
      LET a(3,1)=-1
      LET b(3,1)=0

      LET a(1,2)=1
      LET b(1,2)=-1
      LET a(2,2)=0
      LET b(2,2)=-1
      LET a(3,2)=1
      LET b(3,2)=0

      LET a(1,3)=-1
      LET b(1,3)=1
      LET a(2,3)=0
      LET b(2,3)=1
      LET a(3,3)=-1
      LET b(3,3)=0

      LET a(1,4)=1
      LET b(1,4)=1
      LET a(2,4)=0
      LET b(2,4)=1
      LET a(3,4)=1
      LET b(3,4)=0

      LET e(1,1)=-1
      LET f(1,1)=-1
      LET e(2,1)=-1
      LET f(2,1)=-1
      LET e(3,1)=-1
      LET f(3,1)=-1

      LET e(1,2)=-1
      LET f(1,2)=1
      LET e(2,2)=-1
      LET f(2,2)=1
      LET e(3,2)=-1
      LET f(3,2)=1

      LET e(1,3)=-1
      LET f(1,3)=-1
      LET e(2,3)=-1
      LET f(2,3)=-1
      LET e(3,3)=-1
      LET f(3,3)=-1

      LET e(1,4)=-1
      LET f(1,4)=1
      LET e(2,4)=-1
      LET f(2,4)=1
      LET e(3,4)=-1
      LET f(3,4)=1

      PRINT " square SIERPINSKI gasket I.F.S. "
      PRINT " BY R.L.BAGULA 1 May 2004© copy rights reserved"
      RANDOMIZE
      PRINT " M=";m
      PRINT " n0=";n0
      LET r=2

      PRINT r
      FOR n= 1 TO 8000000
      LET c =RND
      LET d =rnd
      LET l=1+int(c*m)
      LET k=1+mod(n,n0)
      IF k=3 then let s=-1 else LET s=1

      LET x1=e(l,k)*x/r+a(l,k)
      LET y1=f(l,k)*y/r+b(l,k)
      LET x=x1
      LET y=y1
      SET COLOR 255-(255/(m+n0+1))*(l+k)
      IF n>5 THEN PLOT 1920/2+s1*x,1024/2+s2*y
      NEXT n
      END


      --
      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      URL : http://home.earthlink.net/~tftn
      URL : http://victorian.fortunecity.com/carmelita/435/
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