Christopher Alexander approached his fifteen geometric properties from a roughly phenomenological standpoint. They are “fundamental” in the sense that they are sufficiently differentiated from one another for each to warrant its own distinct treatment. It is nevertheless possible to view commonalities among the properties, suggesting that they can be broken down to even more elementary concepts. Alexander himself hinted at this when he proposed a separate set of eleven properties for colour. Some years ago, I even considered a grouping of the properties in terms of their pertinence to information theory.
A few of Alexander’s properties share a characteristic that can be articulated roughly like the space between two (or more) centers is itself a (strong) center. Boundaries is one such property. Alternating repetition and positive space, which also happen to constitute the next two chapters, have the same characteristic as well.
In my information-theoretic meta-categorization scheme, I put boundaries in a separate category (conveying a signal) from alternating repetition and positive space (compression). This demonstrates that there is more than one way to cluster the properties. We expect this, however, since we’re ultimately trying to bucket continuous phenomena like space, colour, and feeling into discrete concepts and conceptual structures.