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Re: Sierpinski

From Ilya Zakharevich <nospam-abuse@ilyaz.org>
Newsgroups comp.lang.postscript
Subject Re: Sierpinski
Date 2011-12-25 01:33 +0000
Organization U.C. Berkeley Math. Department.
Message-ID <slrnjfcvak.km1.nospam-abuse@panda.math.berkeley.edu> (permalink)
References <111db8ba-d74d-4641-9be8-b8396eb7b74a@f11g2000yql.googlegroups.com> <b9b6fdd9-ffa2-4a63-adbf-bb065c1e4f58@p13g2000yqd.googlegroups.com>

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On 2011-12-24, luser- -droog <mijoryx@yahoo.com> wrote:
> Revised and expanded. Snowflakes, triangles, and a big dragon.

Just a hint: I do my Sierpinski in 0.5 setgray.  Then the stipple
pattern of a Laser printer makes the impression of "infinite depth".
Here is the source of one of the problems for the baby math circle:

%!PS
[ /Title  (Sierpinski gasket with a path to find pattern, continue and calc length)
  /Author (Ilya Zakharevich)
  /DOCINFO pdfmark

/inch { 72 mul } def
1 setlinecap
0 setlinewidth
0.5 setgray

/tr_height 3 sqrt 2 div def

% Make triangle height + 0.5 inch border to be paper height
0.5 inch dup translate
10 inch tr_height div dup scale


% depth Sierpinski
/Sierpinski {
  newpath
  0 0 moveto
  1 0 lineto
  0.5 tr_height lineto
  closepath stroke
  dup 0 eq not
  {
    1 sub			% : count
    gsave
    0.5 dup scale
    dup Sierpinski
    1 0 translate
    dup Sierpinski
    -0.5 tr_height translate
    dup Sierpinski		% leaves count : count
    grestore
  } if
  pop				% removes count
} bind def

10 Sierpinski

0.004 setlinewidth
0 setgray

0.5 tr_height moveto
0 0 lineto
0.5 0 lineto
0.375  tr_height 4 div lineto
0.25 0.0625 add tr_height 8 div lineto
stroke

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Thread

Koch snowflake using Lindenmeyer System luser- -droog <mijoryx@yahoo.com> - 2011-12-23 14:32 -0800
  Re: Koch snowflake using Lindenmeyer System luser- -droog <mijoryx@yahoo.com> - 2011-12-24 03:59 -0800
    Re: Sierpinski Ilya Zakharevich <nospam-abuse@ilyaz.org> - 2011-12-25 01:33 +0000
      Re: Sierpinski luser- -droog <mijoryx@yahoo.com> - 2011-12-24 21:22 -0800
        Re: Sierpinski Ilya Zakharevich <nospam-abuse@ilyaz.org> - 2011-12-25 22:49 +0000
          Re: Sierpinski luser- -droog <mijoryx@yahoo.com> - 2011-12-25 19:19 -0800
            Re: Sierpinski Ilya Zakharevich <nospam-abuse@ilyaz.org> - 2011-12-27 20:09 +0000
      Re: Sierpinski tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2011-12-26 21:47 -0500
        Re: Sierpinski Ilya Zakharevich <nospam-abuse@ilyaz.org> - 2011-12-27 20:13 +0000
          Re: Sierpinski tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2011-12-27 16:37 -0500
      Re: Sierpinski tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2011-12-26 22:26 -0500
      Re: Sierpinski tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2011-12-26 23:24 -0500
        Re: Sierpinski Ilya Zakharevich <nospam-abuse@ilyaz.org> - 2011-12-27 20:22 +0000
          Re: Sierpinski tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2011-12-27 16:29 -0500
            Re: [OT] Sierpinski etc Ilya Zakharevich <nospam-abuse@ilyaz.org> - 2011-12-28 22:37 +0000
              Re: [OT] Sierpinski etc tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2011-12-28 19:53 -0500
                Re: Sierpinski etc luser- -droog <mijoryx@yahoo.com> - 2011-12-28 23:35 -0800
                Re: Sierpinski etc tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2011-12-29 12:07 -0500
    ??? using Lindenmeyer System luser- -droog <mijoryx@yahoo.com> - 2011-12-27 22:55 -0800
      Re: ???(broccoli) using Lindenmeyer System luser- -droog <mijoryx@yahoo.com> - 2011-12-31 15:32 -0800

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