Recursive Patterns
In a facial attraction pattern (FAP), recursive aspects can also occur.
A recursive pattern is a pattern within which the same pattern is visible and within that, that pattern is embedded once again. A pattern within a similar pattern within the same pattern. This repetition can go many levels deep.
In terms of software coding, this is an algorithm that calls itself again.
The software function A calls itself (B = copy of A), while procedure A has not yet been completed. Function B calls C (another copy of A) while B has not yet been completed, and so on. After this, C is terminated first, then B is closed, and only then is A completed.
Recursiveness is a basic property of hologrammatic figures.
It would not surprise me if geneticists were to one day find such an algorithm in the DNA structure. This could explain pattern repetition in the face.

Image A: Abstract picture of a Face in a Face in a Face.
Narrowing down Chance
Facial Attractor Patterns come into existence through the following long term process:
Random chance becomes slightly narrowed down towards a specific direction, by accumulation of genetic preferences. This happens through long term genetic evolution within this particular animal species by the mechanism of sexual selection, that recurs in every next generation over and over again.