S'up. (Everything I will say hinges on Physicalism being true)
Rather than attempting to quantify beautiful on a superficial level- through trying to determine patterns in what we observe to be beautiful, why not instead ask whether our beauty can be quantified based on the more objective neural processes in our brains?
Assumedly, every little sense of self and perception we have is a result of chemical reactions in our brain. In that case, even the slippery, subjective concepts such as what we find beautiful can, technically, be reduced to logical, natural and objective processes in our brain.
What I believe is that there is a definite framework for the recognition of beauty, based on this. On a very fundamental level, if past experiences are excluded, then we should, technically, all find the same things beautiful and derive the exact same feeling from it. But, all our perceptions of beauty are derived, and we, as individuals, build upon this framework for the recognition of beauty based on our own experiences (which are imprinted as processes or activities in the brain). But, there are some sources of beauty which are apparently more resistant to change (the golden ratio might be one of them) and still fall within our collective definition of beauty.
Some food for thought: Do different genes between individuals lead to different biological makeups of the human brain? In that case, even on a very fundamental level, there would still be differences in beauty, and perhaps, this would entail that children tend to experience a similar, if not identical, sense of beauty as their parents.
And so, if physicalism is the case, then once neurobiology becomes advanced enough to be able to determine how each individual part of the brain contributes to our consciousness, beauty can be quantified in terms of the processes and activities in our brain. So, if person A finds an object beautiful and person B does not, it is because person A has different processes and activities triggered in his/her brain, and that if such processes are triggered or introduced in person B, that person will feel the exact same thing as person A does.
Of course, this does not answer the question of why we even recognize things to be beautiful, but it provides a means to quantify beauty based on an objective measurement, that of neural processes in the brain.