Summary edit

An attempt at a simple form of a "wheeled" type of Triskelion symbol (containing three double spirals, connected together by spokes on the inside, and which branch out into arcs of a circle partially enclosing the whole figure on the outside). Inspired by various Celtic decorative motifs, but this version is constructed from mathematical Archimedean spirals.

For another effort in this direction, see Image:Wheeled-Triskelion-basic.svg (also enclosed in partial circle). For a more ornate "wheeled" triskelion, see Image:Triskelion-spiral-threespoked-inspiral.svg (enclosed in overall spiral).

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:Triple-spiral-wheeled-simple.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
/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 90 eq phase 270 eq or not{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 .793 def % number of 360 degree turnings to show
/const 3.732 def
/phase 0 def aspiral
double 0 ne{
/sweeps 0.62534 def
/const 2.805 def
/phase 90 def aspiral}if
quadruple 0 ne{/const 0 def
/sweeps 0.95834 def
/phase 180 def aspiral
/sweeps 0.75029 def
/phase 270 def aspiral}if
grestore
%%%%%%%%%%%%%%%%
}def
/extensions{/const 0 def/lower 345 def/incrm 12.48 def
/sweeps 358 360 div def/phase 180 def
gsave centerx centery translate rotf rotate aspiral grestore
/lower 270 def/incrm .4 def
/sweeps 270.41 360 div def/phase 270 def
gsave centerx centery translate rotf rotate aspiral grestore}def
/curvedge{/const 0 def/lower 368.13 def/incrm 11.6 def
/sweeps 392 360 div def/phase 90 def
gsave centerx centery translate rotf rotate aspiral grestore}def
gsave
342 -457 translate -1 1 scale 35.955 rotate
/lower 0 def/incrm 15 def/disp{135 rotf 23.68 sub}def/trnslx{
disp sin neg mul disp cos mul translate}def
gsave
/centerx 304 def/centery 550 def/rotf 5.67 def trnslx
gsave archimdouble grestore extensions curvedge
/lower 0 def/incrm 15 def grestore
gsave
/centerx 634 def/centery 550 def/rotf 125.67 def trnslx
gsave archimdouble grestore extensions curvedge
/lower 0 def/incrm 15 def grestore
gsave
/centerx 469 def/centery 835.7884 def/rotf 245.67 def trnslx
gsave archimdouble grestore extensions curvedge grestore
grestore
341.2207 340.6995 206.87  7.53 90 arc stroke
341.2207 340.6995 233.784 90 -2.575 arcn stroke
341.2207 340.6995 206.87  127.53 210 arc stroke
341.2207 340.6995 233.784 210 117.425 arcn stroke
341.2207 340.6995 206.87  247.53 330 arc stroke
341.2207 340.6995 233.784 330 237.425 arcn stroke
.1 .1 .75 setrgbcolor
341.2207 340.6995 34.375 360 0 arcn fill
1 setgray
341.2207 340.6995 13.75 360 0 arcn fill
1 .925 .75 setrgbcolor 6.875 setlinewidth
341.2207 340.6995 260.698 360 0 arcn closepath stroke
showpage
%EOF

Licensing edit

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.