Another surprise to me. The agate pattern has a preferred z 
direction(1). Said another way, it works best (always?) projected onto 
an x,y plane (a +-z plane object in POV-Ray).

I think it won't much show up - so long as pattern, transform and object 
modifiers manipulations are nearly symmetrical in x,y,z. However, I'm 
not completely sure, there are too many options, combinations...

I'm sure it shows. Now knowing about it, I used the 'feature' in the 
attached image.

#declare Fn00 = function { pattern {
     agate
     warp { turbulence 0.04 octaves 5 omega 0.41 lambda 6 }
     octaves 4    // 6
     omega   0.13 // 0.5
     lambda  1.33 // 2.0
     noise_generator 2
     frequency 0.5
     poly_wave 0.2
     scale 1/3
     rotate x*90
}}

The first turbulence in the warp turbulence list is symmetrical in 
magnitude and effect, but also of the sort to show the z treatment by 
agate. The agate pattern has been oriented for a y up view and 
displacement of the y plane object.

Note! The warp{} block around the initial turbulence is necessary. 
Otherwise the trailing octaves, omega and lambda are applied to it. See 
documentation on bare turbulence vs warp{} wrapped. Mostly, wrap 
turbulence with warp {} to ensure turbulence ordering - and option 
associations.

Bill P.

(1) - At the core it grabs only the z point from 3d space and 'mixes' it 
with a turbulence value so as to change the value distribution to be U 
shaped; to be heavy toward zero and one.

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