Image:Triskelion-spiral-threespoked-inspiral.svg

[edit] Summary

A form of a Triskelion symbol containing three double spirals which branch out into a larger spiral which encloses the whole figure. Inspired by various Celtic decorative motifs, but this version is constructed from mathematical Archimedean spirals. Useful as an example of a "wheeled" type of triskelion. For less ornate "wheeled" triskelions with partially-enclosing circle (instead of enclosing spiral), see Image:Wheeled-Triskelion-basic.svg , Image:Roissy triskelion iron ring signet.png , and Image:Triple-spiral-wheeled-simple.svg .

For other, non-wheel versions of the triskelion or triple-spiral symbols, see Image:Triskele-Symbol-spiral-five-thirds-turns.svg , Image:Triple-Spiral-Symbol-filled.svg , Image:Triple-Spiral-Symbol-4turns-filled.svg , Image:Triskele-Symbol-spiral.svg , or Image:Triple-Spiral-Symbol.svg . For a spiral triskelion with a hollow triangle in the center, see Image:Triskele-hollow-triangle.svg . For versions of a triple-spiral labyrinth, see Image:Triple-Spiral-labyrinth.svg and Image:Triple-Spiral-labyrinth-variant.svg .

SVG version of Image:Triskelion-spiral-threespoked-inspiral.png .

Converted from the following PostScript code:

%!
/archimdouble{
%%%%%%%%%%%%%%%%
% PostScript program to display an Archimedean spiral by approximating
% it with Bezier curves.  Can display a double spiral (two spirals
% rotated by 180 degrees with respect to each other).
%%%  Parameters:
                 % centerx = horizontal coordinate of center of spiral
                 % centery = vertical coordinate of center of spiral
                 % rotf = degrees to rotate
/sepwid 110 def  % width separating successive turnings of spiral
                 % (half this if double spiral is selected)
/incrm 15 def    % insert a curve point after this number of degrees
                 % CHANGE TO 30 EXCEPT AT TRANSITIONS
/double 1 def    % change to 0 to display single spiral
/quadruple 1 def % change to 0 to display single/double spiral only
%%%  Procedures:
/pi 3.1415926535898 def/radians 57.295779513082 def
/sepwid sepwid pi div 2 div def
gsave centerx centery translate rotf rotate
/aspiral{/prevbezy 0 def/first 1 def
    lower incrm sweeps 360 mul{8{dup}repeat
        phase add cos/costh exch def
        phase add sin/sinth exch def
        costh mul radians div/thcosth exch def
        sinth mul radians div/thsinth exch def
        thcosth sepwid mul/x exch def
        thsinth sepwid mul/y exch def
        0 eq phase 90 eq phase 270 eq or and{/slope 999999999 def}{/slope
        sinth thcosth add costh thsinth sub div def}ifelse
        sinth 0 gt sinth 0 eq costh -1 eq and or{/flag -1 def}{/flag 1
            def}ifelse
        /A exch def phase 0 eq phase 180 eq or{A 49.29348 lt A 180 gt
            A 196.273450852 lt and A 360 gt A 368.8301 lt and A 540 gt A
            545.9907 lt and A 720 gt A 724.5217 lt and A 900 gt A
            903.6281968 lt and or or or or or{/flag flag neg def}if}if
        incrm sub 3{dup}repeat phase add cos sepwid mul mul radians div
            /prevx exch def phase add sin sepwid mul mul radians div
            /prevy exch def
        incrm add 3{dup}repeat phase add cos sepwid mul mul radians div
            /nextx exch def phase add sin sepwid mul mul radians div
            /nexty exch def
        /prevdist x prevx sub dup mul y prevy sub dup mul add sqrt pi
            div def
        /nextdist x nextx sub dup mul y nexty sub dup mul add sqrt pi
            div def
        /normaliz slope slope mul 1 add sqrt def
        0 eq{0 0 moveto/prevbezx phase cos nextdist mul def/first 0 def
            }{first 1 eq{x y moveto/first 0 def}{prevbezx prevbezy x 1
            flag mul normaliz div prevdist mul sub y slope flag mul
            normaliz div prevdist mul sub x y curveto}ifelse
        /prevbezx x 1 flag mul normaliz div nextdist mul add def
        /prevbezy y slope flag mul normaliz div nextdist mul add def}ifelse}
    for stroke
    x y moveto x 1 flag mul normaliz div nextdist mul pi mul const mul add y
    slope flag mul normaliz div nextdist mul pi mul const mul add lineto
    stroke}def
/sweeps 1.67 def % number of 360 degree turnings to show
/const 2.315 def
/phase 0 def aspiral
double 0 ne{
/sweeps 1.4584 def
/const 2.621 def
/phase 90 def aspiral}if
quadruple 0 ne{
/sweeps 645.1 360 div def
/const 0 def
/phase 180 def aspiral
/sweeps 555.1 360 div def
/const 0 def
/phase 270 def aspiral}if
grestore
%%%%%%%%%%%%%%%%
}def
68 55 translate
.75 dup scale
gsave
800 0 translate -.75 .75 scale -20.77 rotate
/lower 0 def
/disp{70 rotf -56.801 sub}def/trnslx{disp sin neg mul disp cos mul
translate}def
gsave
/centerx 304 def/centery 550 def/rotf 125.67 def trnslx
  archimdouble
grestore
gsave
/centerx 634 def/centery 550 def/rotf 245.67 def trnslx
  archimdouble
grestore
gsave
/centerx 469 def/centery 835.7884 def/rotf 5.67 def trnslx
  archimdouble
grestore
grestore
.75 setlinewidth
598.996 0 translate -1 1 scale
299.498 327.764 10.3125 360 0 arcn stroke
299.498 327.764 translate
/sepwid 123.75 pi div 2 div def
/const 0 def
/incrm 30 def
gsave
-3.0445 rotate
1.00451 dup scale
/sweeps 3.1 def
/lower 870 def
/phase 60 def aspiral
/phase 180 def aspiral
/phase 300 def aspiral
grestore
gsave
-2.87 rotate
1.00412 dup scale
/sweeps 3.27 def
/lower 930 def
/phase 0 def aspiral
/phase 120 def aspiral
/phase 240 def aspiral
grestore
showpage
%%EOF

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