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The Honeycomb by MakinMagic The Honeycomb by MakinMagic
Created using Ultra Fractal.
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:iconkuzy62:
kuzy62 Featured By Owner Nov 2, 2009  Hobbyist Digital Artist
That is amazing! :omg:

What formula??? :clap:
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:iconmakinmagic:
MakinMagic Featured By Owner Nov 3, 2009  Hobbyist Digital Artist
Hi Dan, thanks !

I'm still tweaking the UF formula privately, but as to the mathematical formula it's the White/Nylander as discussed here:

[link]

And the main iterate is:

r = (magn=sqrt(magn))^@mpwr
th = @mpwr*atan2(zri)
ph = @mpwr*asin(zj/magn)
zri = r*(cos(th)*cos(ph) + flip(cos(ph)*sin(th))) + cri
zj = -r*sin(ph) + cj
magn = |zri| + sqr(zj)

Where the initial value of magn is calculated before entry into the loop. For this particular Julia @mpwr was 10.
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:iconmakinmagic:
MakinMagic Featured By Owner Nov 19, 2009  Hobbyist Digital Artist
For any mathematicians used to maths notation rather than fractal software notation, you should note that |zri| in the above is x^2+y^2 where zri=(x+i*y) i.e. the square of the magnitude of zri.
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:iconmakinmagic:
MakinMagic Featured By Owner Nov 19, 2009  Hobbyist Digital Artist
That smiley should read:
where zri = (x+i*y)
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:iconsilverb:
silverb Featured By Owner Nov 1, 2009
Great piece!
:salute:
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:iconmakinmagic:
MakinMagic Featured By Owner Nov 1, 2009  Hobbyist Digital Artist
Thank you.
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:icongeaausten:
GeaAusten Featured By Owner Nov 1, 2009  Professional General Artist
this has to be viewed large.. its amazing !
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:iconmakinmagic:
MakinMagic Featured By Owner Nov 1, 2009  Hobbyist Digital Artist
Thanks !
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:iconwinklepickers:
winklepickers Featured By Owner Nov 1, 2009
Strong, fascinating forms in a strange world of solidity. :)
I like this.
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:iconmakinmagic:
MakinMagic Featured By Owner Nov 1, 2009  Hobbyist Digital Artist
Thanks.
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:iconjimpan1973:
Jimpan1973 Featured By Owner Oct 31, 2009  Hobbyist Digital Artist
That is totally awesome!
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:iconmakinmagic:
MakinMagic Featured By Owner Nov 1, 2009  Hobbyist Digital Artist
Thanks.
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:iconboot-cheese-3000:
boot-cheese-3000 Featured By Owner Oct 31, 2009
man this is trippy, the colors and it looks all warped and stuff......
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:iconmakinmagic:
MakinMagic Featured By Owner Nov 1, 2009  Hobbyist Digital Artist
Thank you.
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:iconboot-cheese-3000:
boot-cheese-3000 Featured By Owner Nov 1, 2009
yeah what was you schmokin' fly guy? :laughing:
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Submitted on
October 31, 2009
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398 KB
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