The Chaos Game

chaos.ps

/randomseed { (/dev/random)(r)file read pop srand } bind def

/random { % max  =>  0<num<max
    rand 16#7fffffff div mul
} bind def

/genpoly { % n => [ [x0 y0] ... [xn-1 yn-1] ]
    2 dict begin
    /n exch def
    /da 360 n div def
    [
        0 1 n 1 sub {
            da mul
            dup cos
            exch sin
            2 array astore
        } for
    ]
    end
} bind def

/2sub { % x1 y1 x0 y0 => dx dy
    exch % x1 y1 y0 x0
    3 1 roll % x1 x0 y1 y0
    sub % x1 x0 dy
    3 1 roll % dy x1 x0
    sub % dy dx
    exch
} bind def

/drawpoint {
    gsave
        currentpoint currentlinewidth 2 mul
        0 360 arc fill
    grestore
} def

/iterate {
    poly n random cvi get aload pop
    currentpoint 2sub
    exch frac mul
    exch frac mul
    rmoveto
    drawpoint
} def

/chaos { % n frac iterations => -  (create path)
    4 dict begin
    /iterations exch def
    /frac exch def
    /n exch def
    /poly n genpoly def

    0 0 moveto     % find random start point
    0 0
    poly {
        aload pop
        4 2 roll 2sub
        .5 random mul exch
        .5 random mul exch
        2 copy rmoveto
    } forall
    rmoveto

    iterations //iterate repeat

    end
} bind def

/setscale { % n => -
    dup dup scale
    1 exch div currentlinewidth mul setlinewidth
} bind def

/chaoschart {
    0 1 4 { % i
        0 1 3 { % i j
            gsave 
                1 index % i j i
                2 copy
                1 add exch 1 add exch
                translate % i j i
                .3 .3 scale
                %exch 4 mul add 3 add % i n   calc n from i and j
                %pop pop 3            %       all triangles
                pop pop n            %       use global n
                frac iterations chaos stroke
                /frac frac fracdelta add def
            grestore
        } for
        pop
    } bind for
} def

randomseed
currentlinewidth .5 mul setlinewidth
120 setscale
%/frac 3.14159 2 mul 3 div def
%/frac .5 def
%/frac .6199 def
/frac .4 def
/fracdelta .05 def
/iterations 10000 def
/n 5 def

chaoschart
showpage
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Revision 2 draws different fractional lengths in each small drawing, instead of different polygons.