I'm certain the reasons these patterns are important extend beyond the one I choose to illustrate, nevertheless this one is incredibly pertinent to a certain argument I have ensued between me and my mirror, AND any unlucky passerby who is caught in between.
Realizing patterns is a product of the original, purest form of art: making relevant connections between seemingly unrelevat concepts.
more about this form of art has been explained here:
http://curiousityandscience.blogspot.com/2012/03/chill-your-art-out.html
First let me begin with this diagram: