File:Interlocked triskelions and partial triskelions in circle.svg
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[edit]| Description | An interlocking configuration of three triskelion shapes (which meet at a central point) and six partial triskelions, contained within a circle. This pattern is generated by means of Archimedean spirals, and is loosely inspired by the central design of the Aberlemno cross stone. This is based on an overall quasi-tessellation of the plane with Archimedean-spiral triskelion shapes (leaving small concave triangular gaps between them) -- see File:Triskelion-quasi-tessellation.svg) -- which is cropped within a circle. The yellow, blue, and red areas along the edge of the circle are cropped triskelions from the original tessellation, but each of the grey areas joins parts of two triskelions from the original tessellation. This is why the pattern in this image requires four positive colors (so that no shapes of the same color are next to each other), while the File:Triskelion-quasi-tessellation.svg pattern requires only three. According to George Bain, the triskelions in the original Aberlemno cross design do not have constant-width arms (as is the case when using Archimedean spirals)... For other variations on the theme of seven three-fold spirals, see File:Seven-sixfold-spirals.svg and File:Seven-sixfold-spirals-stroked.svg . | ||
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| Source |
Converted from the following self-authored PostScript vector source code: %!
/archimtriple{
%%%%%%%%%%%%%%%%
% PostScript program to display an Archimedean spiral by approximating
% it with Bezier curves. Can display a triple spiral (three spirals
% rotated by 120 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 30 def % insert a curve point after this number of degrees
% /sweeps % number of 360 degree turnings to show
/triple 1 def % change to 0 to for non-triple inner spiral
%%% Procedures:
/pi 3.1415926535898 def/radians 57.295779513082 def
/sepwid sepwid pi div 2 div def
gsave centerx centery translate rotf rotate
/aspiral{/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
phase 120 eq phase 300 eq or{A 10 lt A 80 gt A 100 lt and
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/prevbezy
phase sin 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}def
%%% If different sweeps parameter for other spirals, define here:
X grestore
%%%%%%%%%%%%%%%%
}def
306 396 translate
.54 dup scale
180 rotate
1 -1 scale
/lower 0 def
/X {/sweeps 1.26 def/phase 0 def aspiral
triple 0 ne{/phase 120 def aspiral
/phase 240 def aspiral} if}def
/centerx 0 def/centery 0 def/rotf 0 def
archimtriple
/X {/sweeps 1.26 def/phase 0 def aspiral
triple 0 ne{/sweeps 1.26 def/phase 120 def aspiral
/sweeps 1.3 def/phase 240 def aspiral} if}def
/edge1{/lower 465 def/incrm 15 def/phase 240 def/sweeps 1.45 def gsave
centerx centery translate rotf rotate aspiral/lower 510 def /incrm 15 def
/sweeps 1.56 def/phase 0 def aspiral grestore/incrm 30 def/lower 0 def}def
/centerx 0 def/centery 256.666667 def/rotf 0 def
archimtriple edge1
/centerx -222.279854 def/centery -128.333333 def/rotf 120 def
archimtriple edge1
/centerx 222.279854 def/centery -128.333333 def/rotf 240 def
archimtriple edge1
/X {/sweeps 1.26 def/phase 0 def aspiral
triple 0 ne{/sweeps 1.12 def/phase 120 def aspiral
/sweeps 1.17 def/phase 240 def aspiral} if}def
/edge2{/lower 445 def/incrm 20 def/sweeps 1.36 def/phase 240 def gsave
centerx centery translate rotf rotate aspiral/lower 410 def/incrm 24/sweeps
1.28 def/phase 120 def def aspiral grestore/incrm 30 def/lower 0 def}def
/centerx 0 def/centery -256.666667 def/rotf 0 def
archimtriple edge2
/centerx -222.279854 def/centery 128.333333 def/rotf 240 def
archimtriple edge2
/centerx 222.279854 def/centery 128.333333 def/rotf 120 def
archimtriple edge2
0 0 341.333333 -7 12 arc stroke
0 0 341.333333 113 132 arc stroke
0 0 341.333333 233 252 arc stroke
0 0 341.333333 -73 -52 arc stroke
0 0 341.333333 47 68 arc stroke
0 0 341.333333 167 188 arc stroke
1 0 0 setrgbcolor
0 0 377.425667 0 360 arc closepath stroke
showpage
%EOF |
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| Author | AnonMoos | ||
| Permission (Reusing this file) |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 01:21, 5 September 2022 | | 600 × 600 (12 KB) | Smasongarrison (talk | contribs) | slimmed down with svgomg // Editing SVG source code using c:User:Rillke/SVGedit.js |
| 22:51, 10 April 2021 |  | 600 × 600 (16 KB) | AnonMoos (talk | contribs) | {{Information |Description=An interlocking configuration of three triskelion shapes (which meet at a central point) and six partial triskelions, contained within a circle. This pattern is generated by means of Archimedean spirals, and is loosely inspired by the central design of the Aberlemno cross stone. This is based on an overall quasi-tessellation of the plane with Archimedean-spiral triskelion shapes (leaving small concave triangular gaps between them) -- see [[:File:Triskelion-quasi-t... |
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