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I just tried out Kalles Fractaler.
Wow.
+ It's not just a fast zoomer. More important is that program alsou is very fun to use. Zoom somewhere and then allow program to search for minibrot. And it don't crashes as I expected;) Maybe a new word in world of fractals.

- Impossible to save image as .png or .bmp. If I'm correct saving as .jpg allways create some loss even with 100%.

I have a few ideas (you 'll hate me, whatever ). In Ultra Fractal I did few colour methods including modified Pauldebrots Smooth which I think should be very much like this smoothing.
UF have an operator #random which returns a random value (between 0 and 1) for each pixel. Then final colourvalue = abs( tanh(0.04 *#random) + colourvalue) gives the image slight suede texture. Works nicely if image is too much plain.

Randomly generated RGB colours allways have strange looks becouse colour wheel have unnaturaly large proportions of blue. To overcome this I simply did usophisticated operation chanellB=chanellB*0.8 . Throught this yellows the whites. Or maybe some hyperbolic tangent, power or sigmoid function could decrease middle values without decreasing high values. Realy hadn't tested, I like cousy yellowing looks.
With UF smoothings hade used to have log as transfer function / handling of the iteration count values and alsou a sigmoid function ix=4*ix/(3+abs(ix)) throught of corse UF have different approach to colours. UF and most of other escape time looks slightly outdated.

Could I suggest more formulas. All of the included formulas are kind of versions of burning ships. Other zoomable formulas I know:
z=z*sinh(z)-c^2 or generalised  z=z^(n-1)*sinh(z)-c^n  (like mandelbrot but with a julia sets like objects in every level of zoom and minibrots in these objects) Like this:

(insides are coloured by newton colouring in Chaos pro, there is no analog in UF but not so great eather just a rainbow)
https://www.youtube.com/watch?v=CDlJjy9TybA (https://www.youtube.com/watch?v=CDlJjy9TybA)

or a more square like version of burning ship:
x2=x*x + y*y +cx
y2= -2.5x*y +cy

And then with or without:
x2=abs(x2)
y2=abs(y2)


Did a fast Ultra Fractal examples with a parameters:

(http://www.ljplus.ru/img4/a/s/asdam/mbrot1.jpg)
(http://www.ljplus.ru/img4/a/s/asdam/mbrot3.jpg)


mbrot1 {
fractal:
  title="mbrot1" width=1024 height=400 layers=1
  credits="Alef;12/4/2014;Kerry Mitchell;8/2/2002"
layer:
  caption="Layer 1" opacity=100 method=multipass
mapping:
  center=0.380283769797615/0.361662506821665 magn=8347.7907
  angle=4.857
formula:
  maxiter=100000 percheck=off filename="Standard.ufm"
  entry="Mandelbrot" p_start=0/0 p_power=2/0 p_bailout=10000.0
inside:
  transfer=none filename="Standard.ucl" entry="Default"
outside:
  density=1.025 transfer=linear filename="em.ucl"
  entry="Pauldebrots_Smooth" p_convergent=no p_esm=no p_alt=no
  p_perfix=1.0 p_zmax=100 p_power=2 p_fit=yes p_fittimes=1.0
  p_fitminit=51 p_fitmaxit=8700 p_transfer=Sigmoid p_transpower=3.0
  p_bailout=10000.0 p_userandom=yes p_hyperandom=0.04
gradient:
  comments="slightly changed standart. IMHO good sky." smooth=no
  rotation=23 index=22 color=6303744 index=86 color=12085789 index=190
  color=16777197 index=279 color=33023 index=365 color=512
opacity:
  smooth=no index=0 opacity=255
}


mbrot3 {
; copyright Kerry Mitchell 15sep98
; 
; sample image to illustrate
; embossing effect
fractal:
  title="mbrot3" width=1024 height=512 layers=1
  credits="Alef;12/4/2014;Kerry Mitchell;9/15/1998"
layer:
  caption="Layer 1" opacity=100 method=linear transparent=yes
mapping:
  center=-0.81810721128409/0.19884197484006 magn=4118.0018
  angle=34.1619
formula:
  maxiter=1000 percheck=off filename="Standard.ufm" entry="Mandelbrot"
  p_start=0/0 p_power=2/0 p_bailout=10000.0
inside:
  transfer=none
outside:
  transfer=linear filename="em.ucl" entry="WaveTrichrome"
  p_palette="Fractal Explorer like" p_seed=1 p_orbits=None
  p_switchRB=no p_switchRG=yes p_colmethod="With counter"
  p_naturalise=yes p_postfn="1- None" p_userandom=yes
  p_hyperandom=0.04 p_lightR=0.7 p_scalarR=0.7 p_lightG=1.2
  p_scalarG=1.2 p_lightB=0.25 p_scalarB=0.25
gradient:
  comments="slightly changed standart. IMHO good sky." smooth=no
  rotation=1 index=0 color=6303744 index=64 color=12085789 index=168
  color=16777197 index=257 color=33023 index=343 color=512
opacity:
  smooth=no index=0 opacity=255
}
 

Hahaha
Well, I have had my share of crashes during this 1.5 year of KF with perturbation.

Colors: Have you tried the random RGB Waves, ("Palette Waves")?
More formulas: Indeed! I'd love to be able to do Julias. But they need a lot of analyze before being able to be implemented with perturbation (and I failed the Julias...)
And trigonometry, sinh etc, I guess is not something I can achieve.
But your 3D effect in the other thread is awesome, thanks a lot for that suggestion.
That is something I want to implement!
(I only have effort to do what I feel interesting myself. Maybe I am selfish, but I did share the code ;) )