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I just played with mandelbulb.frag and decide to post frag file. It is very similar to the gnarl 3d but it is not really gnarl   I added z.x=abs(z.y) in DE(vec3 pos). The idea is not mine, i found the same change on DA - originally it was z.x=cos(z.x). It can be changed to z=abs(z.y). Maybe somebody will be interested and will make "really" 3D gnarl.

Totally different from gnarl but nice

of course is possible as heightfield
You simply calculate the formula for x and y, you extract the magnitude then for the DE add to z that mag - edventually corrected with some log()

Example
magold = x*x + y*y;
For (i=0; i<16; i++) {
Xn = x - 0.1 sin(y + 5 sin (2y-0.2*x)); yn = ...; // pick whatever you like with sin cos etc add more sines do it yourself
X= xn; Y= yn;
}
Mag = Magold - x*x - y*y;
Mag = log( 1.5+ mag); // smooth
Return z-Mag;

DarkBeam, i'm really not sure what to do with your formulas in fragmentarium  I do not know glsl or other programming language 
So i write that

float Mag(vec3 pos) {
vec3 z=pos;
int i=0;
float magold = z.x*z.x + z.y*z.y;
for (i=0; i<16; i++) {
float xn = z.x - 0.1* sin(z.y + 5*sin(2*z.y-0.2*z.x));
float yn = z.y - 0.1* sin(z.x + 5*sin(2*z.x-0.2*z.y));
z.x= xn; z.y= yn;
}
float mag = magold - z.x*z.x - z.y*z.y;
mag = log(1.5+ mag); // smooth
return z-mag;
}

How add Mag to DE?


Patryk Kizny, it was long time ago, used first mod by knighty with "3DKn-1.0.0.frag"

  I tried to do as you say before asking you. So i got very very smooth mandelbulb like glued balls. Something wrong.
Maybe i wrote something incorrectly. How add mag to z? DE in mandelbulb already has a return. And as i understand, return z-mag must be replaced with something.

I am sorry, i don`t know what to do with this code...
What means ?

Okay, i get result... if i may say... It looks terrible    FudgeFactor less than 0,01 for decrease noise

upd.: Okay. With pseudo-kleinian it looks much better! Thank you for gnarl in Frag!

Spend some time played with gnarl on a simple surface. To understand how it works. And i find that geometry of spirals is perfect and may be changed by different variables.
So, all that related to 3D - is bad especially when increases height, when 3d small it looks not so bad.
- need very low fudge factor(0.2-0.01). It follows that we need a lot of maxraysteps (2000-4000), or reduce detail, or both.
- shadows are noisy with crazy banding ever when dithering=1. Normal view when detail=2-2.5, so it`s too much.
Maybe you can tell how optimize code...
Interesting result when return z.z-abs(mag);

A few renders. I attached frag with some presets and my version of renderer.