Looking out of an airplane window, it’s quite obvious what structures are natural and what structures are manmade. The natural structures are curvy, chaotic, yet recursive. They take very, very complex patterns and project them to us in a very simple way. The man-made structures are the opposite – they take simple underlying shapes (squares, straight lines, perfect circles) and combine them in haphazard, unpredictable, and hard-to-encode ways. Looking at them is to look at a chaotic jumble of ordered elements.
By the way, this is also what mathematicians mean by an “elegant” solution – a simple formula that encodes much complexity and variance underneath.
Of course, beauty is relative because we have different patterns stored that we can match against. Therefore it’s possible for a pattern that seems elegant and simple to one versed in Middle-Eastern art to appear overly complex and non-recursive to one who is mostly used to Western Art.
The brain loves to complete patterns. We do it for survival value all the time to predict the environment around us. But it also completes patterns for play (I suspect that we can’t turn this ability off). There is something aesthetic in completing a pattern in a casual, easy way. That’s why we enjoy listening to music – we can predict the next note, which seems just right, before it occurs. Once we know the song too well and the thrill of completion goes away, the music is “stale,” and we have to move on. Some of the best music is recursive on many levels, so that the patterns extend in time, amplitude / volume, across instruments, across sections, etc.. Engaging multiple senses heightens the experience – for people who know how to dance to a given beat, their brain can complete the patterns across the aural and corporal senses simultaneously. For those of us who can’t dance, the frustration of one pattern which cannot be completed overwhelms the joy from the other.
I still don’t get a lot of modern art though. It seems that after the invention of photography, painting lost its objective measure (realism) and devolved into inbred conversations between generations of artists and successive responses (as philosophy has been doing for centuries).