Christopher Alexander, in The Nature of Order, frequently references ancient Turkish prayer carpets. I wasn’t, and still am not a fan of these artifacts, but as I was searching for an example to use in this post, I was surprised to find, that though there are many images online, finding one that is good was difficult. I was finally able to find one that demonstrated the idea of corners, but not one that felt beautiful … so this will have to do:
Following is a cutout section (marked in the picture above):
Borders are one of the key features in these carpets and this particular carpet illustrates how patterns are used to created borders. These specific patterns (there are four borders depicted in the image) are weak and uninteresting (because I could not find good ones with enough resolution for this demonstration) but they are enough to demonstrate corner. What happens when you continue these patterns? when you repeat them and eventually reach the corners? Here is what happens:
Roughness appears. They do not match up perfectly and each corner needs to be specifically and locally resolved. This king of roughness is typical in living structures. When an underlying pattern comes into being in a specific context it meets and responds to that context. A leaf on a tree is has a specific underlying pattern, but every leaf grows on a specific place on a branch that is exposed to light and wind and in relation to other leaves and other branches. It grows uniquely in response to its settings and conditions.
When we approach this with a mental / logical mindset (and a correlated sense of aesthetics) we do not arrive at such results. Imagine a graphic designer using software to mimic such a carpet. What is likely to happen is that when the pattern does not converge perfectly in a corner, the designer will go back and change the pattern or overall scale … find some way to make the corner work out (continuing the pattern but generating exacting / symmetric / repeated results). The result is that the carpet (or design) becomes defined by the corners instead of the pattern (its source of life). The corners are no longer a natural meeting place of patterns. The corners become the center. Leaves become mathematically identical … and life diminshes.
I find this kind of mental-overriding of naturally emerging patterns is … well … something we need to be attentive to when shaping the tapestry of our individual and communal lives.
Update Dec 30, 2017
I’ve started reading volume one again and I came across this example of Persian architecture which Alexander mentions. It is a spectacular expression of corners and so much more – a feeling of endless patterns that emerged from a singular point in space and time. Clik on the picture once to go the file and then another time to zoom in and get a closer look at the astonishing detail. Source Wikipedia
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[…] Often the border of ancient carpet is ‘irregular’ where it goes round the corner, that is the design breaks, and the corner seems ‘patched together.’ This does not happen through carelessness or inaccuracy. On the contrary, it happens because the weaver is paying close attention to the the positive and negative, to the alternating repetition of the border, to the good shape of each compartment … To keep all of them just right along the length of the border, some loose and makeshift composition must be done at the corner. […]