Using Z-Transformations

So far Z-Transformations are nothing special. For me they act as a counterpart to C-Transformations.
Like for C-Transformations this term is made up by me, and I do not know if a similar approach has already been made.
Like with C-Transformations the usage of Z-Transformations results in new fractal images out of an existing one.
To use Z-Transformations I have changed Tierazon2 to be able to alter any image using 5 stages with 10 simple functions each stage,
which results in 100000 possible combinations. (The same I did with C-Transformations).
On the left are links to examples.
Below is shown how the Z-Transformations are used within the classical approach.
The perfectness of a perfect apple manikin set seems to be invariant in respect to Z-Transformations,
if the generation function is in the form f(z) + c.

i.e. functions, where z is multiplied with c, like in f(z,c) = z2c2 + zc the perfectness is not preserved.
Anybody welcome who can give me the reason why ;)