In Search Of Language

I've always been interested in communciation between any two unique beings with enough cognitive skills as well as how a common language is developed.  The pool of beings who speak this language grows as time goes on and at some point, the origin of that language is lost in antiquity.  I also have long pondered the question of how we, earth creatures can communicate with extra-terrestrials if contact is made at some point.  I believe that the method that will work will need to have both a solid mathematical basis as well as a simple visual interface.  After all, language really is just a construct of symbols and combinations of symbols that a group of users share.  Language also exists to allow man to talk to machine.  Computer languages at the lowest level consists of simple binary instructions to electronic switches.  At the next level, groups of predefined binary instructions form a single available directive to accomplish a complex series of tasks.  Define enough of these stringed-directives and you have a words and soon enough, a complex vocabulary.  At the highest level, you end up with what you have in modern computers, GUIs.  Since I don't have any formal art training, I continually struggle to communicate my ideas to others who are versed in the language they teach at art school.  I am more comfortable when speaking in the language of the natural sciences and mathematics.  So I had come up with several constructs that are relatively simple ways of representing visually a number system.  The real beauty for me is the existence of hidden mathematical structure within the seemingly visual random image.  And unless the viewer is cognizant of the decoder ring, they will not see its inherent elegance.  This had always fascinated me in the natural world from Newtonian mechanics describing binary stars to statistics methods explaining gas behavior.  As with my series of frameworks, the observer needs to find that mathematical pattern in order to see that there is hidden order underneath all that mess.  (Above is a representation of the 16 unique numbers using permutations of diagonal lines over spatial compartments of two sizes.  A common start-of-series and end-of-series patterns bookend any possible series consisting of any combination of the inner 16.)