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Gyllene penta
 

 

 

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Description ===== Geometriska förhållanden =====

Bilden ovan uppvisar ett antal intressanta mått och förhållanden som är starkt knutna till det sv:gyllene snittet, en sv:naturlig konstant som motsvaras av talet sv:fi eller (1,0 + sv:sqrt(5,0)) / 2,0 (notera kopplingen till talet fem). Några exempel:

  • orange - ljusblå = mörkblå.
  • ljusblå / orange = mörkblå.
  • Ljusblå / mörkblå = orange.
  • Ljusblå + mörkblå = orange.
  • Grön + mörkblå = ljusblå.
  • Grön + orange = 2 · ljusblå.
  • Grön + 2 · mörkblå = orange.
Bakgrundsbilden

Bakgrunden visar fraktalen "phi´V", (eng; phi = fi, five = fem, romerka siffran 5 = V). Fraktalen är av sv:IFS-typ och bygger på fem olika sv:transformationsregler där sv:positionsförändringen är olika i varje regel och ligger på en cirkel med 72° intervall på samma sätt som femuddsstjärnans spetsar gör. sv:Skalningen är densamma i alla reglerna och motsvarar sv:längden på den gröna linjen, ca 0,3891 eller 2,0-fi eller (fi -1,0)², vilket tydligt går igen i bilden där varje ny nivå har just det storleksförhållandet jämfört med den tidigare nivån, (jämför grön linje med ljusblå linje). Någon sv:rotation har däremot inte brukats.

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Kategori:Bilder av fraktaler
Date
Source
Author User Solkoll on sv.wikipedia
Permission
(Reusing this file)


Image: User:Solkoll.
Graphical illustrations made from mathematical algorithms, (well, some of them are "handcrafted" =)
Public domain This work has been released into the public domain by its author, Solkoll. This applies worldwide.
In some countries this may not be legally possible; if so:
Solkoll grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

More images I have made from maths:

See also: Solkoll 2D & Solkoll 3D


Gyllene penta.jpg

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Originally from sv.wikipedia; description page is (was) here * 27 juli 2004 kl.14.30 [[:sv:User:Solkoll|Solkoll]] 512x512 (55 205 bytes) <span class="comment">(kommer)</span>

(Uploaded using CommonsHelper or PushForCommons)



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