The Purpose of 'Mobius' & 'Mobius Inverse' Pre/Post Transforms in Chaotica

[Fractalcathedral]

So I've been noticing that Chaotica, when creating New Random Worlds always applies a Pre-Transform of 'Mobius' and a Post-Transform of 'Mobius Inverse', with the exact opposite parameters. (negative numbers instead of positive).

But when you create a new Iterator, it doesn't have these, for whatever reason.

I've found that you can start tweaking these values and it's a quick way to get small-scale variations on a fractal. This is a neat function, but is it the only function here? Trying to Google this leads to a wormhole of mathematics.

 https://en.wikipedia.org/wiki/M%C3%B6bius_inversion_formula

Does anyone have any background on these guys or their function, as it applies, practically, to fractals?