File:Box or Vicsek Fractal 4-iterations.svg
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Box_or_Vicsek_Fractal_4-iterations.svg (SVG file, nominally 1,154 × 560 pixels, file size: 72 KB)
[edit] Summary
Four iterations of a "box fractal" or "Vicsek fractal", derived by iteratively replacing a square with a saltire or cross of five smaller squares on a 3-by-3 subgrid.
Top: Four iterations of the saltire form of the fractal.
Bottom: Four iterations of the cross form of the fractal. The second iteration is a form of the "cross crosslet" symbol of traditional heraldry.
See also File:Box_fractal.png .
Self-made graphic, converted from the following Vector PostScript source code:
%!
.5 dup scale/sq{3 mul exch 3 mul exch moveto 3 0 rlineto 0 3 rlineto -3 0
rlineto closepath fill}def/X{0 1 sq 1 1 sq 2 1 sq 1 0 sq 1 2 sq}def/T{0 0 sq
1 1 sq 2 2 sq 0 2 sq 2 0 sq}def/x{0 1 X1 1 1 X1 2 1 X1 1 0 X1 1 2 X1}def/t{0 0
T1 1 1 T1 2 2 T1 0 2 T1 2 0 T1}def/X1{9 mul exch 9 mul exch gsave translate X
grestore}def/T1{9 mul exch 9 mul exch gsave translate T grestore}def/X2{27 mul
exch 27 mul exch gsave translate x grestore}def/T2{27 mul exch 27 mul exch
gsave translate t grestore}def/xx{0 1 X2 1 1 X2 2 1 X2 1 0 X2 1 2 X2}def/tt{0
0 T2 1 1 T2 2 2 T2 0 2 T2 2 0 T2}def/X3{81 mul exch 81 mul exch gsave
translate xx grestore}def/T3{81 mul exch 81 mul exch gsave translate tt
grestore}def/sqq{/s exch def 1 .7 .8 setrgbcolor 0 0 moveto s 0 rlineto 0 s
rlineto s neg 0 rlineto closepath fill 0 setgray}def
gsave 10 10 translate 27 dup scale 9 sqq X 0 11 translate 9 sqq T grestore
gsave 307 10 translate 9 dup scale 27 sqq x 0 33 translate 27 sqq t grestore
gsave 604 10 translate 3 dup scale 81 sqq xx 0 99 translate 81 sqq tt grestore
gsave 901 10 translate 243 sqq 0 1 X3 1 1 X3 2 1 X3 1 0 X3 1 2 X3 0 297
translate 243 sqq 0 0 T3 1 1 T3 2 2 T3 0 2 T3 2 0 T3 grestore showpage
%EOF
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 08:11, 21 August 2009 | | 1,154×560 (72 KB) | AnonMoos (Talk | contribs) | (Four iterations of a "box fractal" or "Vicsek fractal", derived by iteratively replacing a square with a saltire or cross of five smaller squares on a 3-by-3 subgrid. Top: Four iterations of the saltire form of the fractal. Bottom: Four iterations of t) |
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