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File:Mathematical-polar-equation-flowers.svg

Original file ‎(SVG file, nominally 642 × 606 pixels, file size: 126 KB)

Description

Mathematical based floral ornaments, derived from the polar coordinates equation r=b+sin(aθ), which is a slight generalization of the Limaçon and Rose curves.

  • Top left: curve with a=5 and b=1.25, non-self-intersecting
  • Top right: curve with a=(5/2) and b=1.08, single-level self-intersecting
  • Bottom left: curve with a=(5/3) and b=1.08, two-level self-intersecting
  • Bottom right: curve with a=(5/4) and b=1.08, three-level self-intersecting

The self-intersecting curves are displayed with "even-odd" fill algorithm.

For other patterns made with the quasi-Limaçon/Rose equation r=b+sin(aθ), see File:Interlaced-Triangles Brunnian-link alternate.svg and File:Quinquetra-interlaced-alternate.svg. For other abstract symmetrical floral ornaments, see Image:Retro-flower-ornaments.svg and Image:Five petal flower icon.svg .
Date
Source

Self-made image, converted from the following four-page vector PostScript source code: 

%!
/A{300 396 translate 75 dup scale}def/w{d mul res
div/th exch def th 5 mul d div/x exch def x sin ecc
add th cos mul x sin ecc add th sin mul}def/B{0 w
moveto 1 1 360 res mul{w lineto}for closepath}def
A/d{1}def/ecc{1.25}def/res{5}def B fill showpage
A/d{2}def -18 rotate/ecc{1.08}def B eofill showpage
A/d{3}def 36 rotate B eofill showpage
A/d{4}def 18 rotate B eofill showpage
%EOF
Author AnonMoos
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(Reusing this file)
Public domain 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.

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Date/TimeThumbnailDimensionsUserComment
current23:32, 20 July 2009Thumbnail for version as of 23:32, 20 July 2009642 × 606 (126 KB)AnonMoosMathematical based floral ornaments, derived from the polar coordinates equation r=b+sin(aθ), which is a slight generalization of the Limaçon and Rose curves. *Top left: curve with a=5 and b=1.25, non-self-in
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