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Some more

Kharakov

Quantum Hot Dog
Joined
Aug 3, 2000
Messages
4,371
Location
OCCaUSA
Basic Beliefs
Don't step on mine.
"normal":

\(r=\sqrt{x^2+y^2+z^2}\)
\(\phi=\arctan(y/x)=\arg (x+yi)\)
\(\theta=\arctan(\sqrt{x^2+y^2}/z)=\arccos(z/r)\)

pine tree (I've thought the math makes more sense for a long time, and it does make smoother fractals when combined with the other formula mods):

\(r=\sqrt{x^2+y^2+z^2}\)
\(\phi=\arctan(z/y)=\arg (y+zi)\)
\(\theta=\arctan(\sqrt{y^2+z^2}/x)=\arccos(x/r)\)


The main difference is the "normal" formula rotates [x vs. y] and [(x and y) vs. z] and the pine tree version rotates [(x vs. (y and z)] and [y vs. z].
 
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