Deviation Actions

MakinMagic's avatar

The Honeycomb

By MakinMagic
18 Favourites
Created using Ultra Fractal.
Image details
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1280x960px 397.76 KB
© 2009 - 2021 MakinMagic
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kuzy62's avatar
That is amazing! :omg:

What formula??? :clap:
MakinMagic's avatar
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:


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.
MakinMagic's avatar
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.
MakinMagic's avatar
That smiley should read:
where zri = (x+i*y)
silverb's avatar
Great piece!
MakinMagic's avatar
GeaAusten's avatar
this has to be viewed large.. its amazing !
winklepickers's avatar
Strong, fascinating forms in a strange world of solidity. :)
I like this.
Jimpan1973's avatar
That is totally awesome!
boot-cheese-3000's avatar
man this is trippy, the colors and it looks all warped and stuff......
MakinMagic's avatar
boot-cheese-3000's avatar
yeah what was you schmokin' fly guy? :laughing:
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