The Fifteen Fundamental Properties of Living Structure. 4. Alternating Repetition

17 July 2010

[The fullest available description of the fifteen fundamental properties of living structure can be found in the four volumes of The Nature of Order — particularly Book One, The Phenomenon of Life (NOPL) . The argument is that living structure, wherever it appears, is composed of fundamental structural features — roughly fifteen of them, at least. Living structure, according to the argument, is in fact unlikely to be discovered lacking too many of these fifteen properties. They are consistently present. The discovery of these properties is the result of decades of attentive observation by architect, builder, and author Christopher Alexander.

The aim of these observations — to better understand the nature of things around us, the order of life, in order to participate in its construction — is not one that should be discarded. Instead, we can cultivate it. One way available to anyone is to simply notice with clear-eyed joy those things that give one life, no matter how small they are, and to welcome the idea that the life they give is real.]

Waves, and the troughs between the waves: alternating repetition.

Alternating Repetition is one of the most pervasive characteristics of living structure. It occurs in almost every plant, every insect, in atomic structures, in cloud formations, in mountain ranges, in waves of every sort — and in many of the most beautiful (and ordinary) artifacts of human creation.

The weave of a basket.

Alternating repetition in a pine cone: overlapping tiers of tongues. Notice also the Boundaries at the outer edge of each tongue, and the Strong Centers throughout, from the cone as a whole to the sharp tips of its tongues... (click on image to better appreciate the presence of the boundaries)

[Read more on Boundaries.  Read more on Strong Centers.]

Alternating repetition in an arbor creating an oscillating play of light.

Alternating repetition in the pattern on the backs of these cicada-like visitors which frequent our bodies throughout the day: lines and trapezoids.

Alternating repetition is to be distinguished from simple repetition. In simple repetition, a single element is simply repeated over and over again. In alternating repetition, by contrast, two elements, each living centers in their own right, repeat after one another, enlivening each other, and generating an intensified field effect throughout the structure. So there is the dead repetition of elements on one hand, and the enlivening repetition of living centers on the other.

In nature most of the repetitions which occur are alternating rather than simple. Repetition itself of course occurs because there are only a limited number of archetypal forms available, and the same ones repeat over and over again, whenever the same conditions occur. Atoms repeat in a crystal lattice, waves on the surface of water repeat; cloud forms repeat in cirrus; mountains in a mountain range repeat; so do the trees in a forest, leaves on a tree, …cracks in a piece of dried up mud, petals on a flower, flowers on a bush.

In most of these cases of natural repetition, the repeating units do alternate with a second structure, which also repeats. When atoms repeat, so do the spaces which contain the electron orbits; when waves repeat, so do the troughs between the waves; as mountains repeat, so do the valleys; when the trees in a forest repeat, so do the open patches of undergrowth where more light falls; when leaves repeat, so do the spaces between the leaves that all the sun to reach the leaves; when cracks in mud repeat, so do the coherent and harder units of the uncracked mud between them; when petals in a flower repeat, so do the sepals which lie behind the petals and overlap them… [etc.] (NOPL, 257-8)

A trillium.

It is important to remember how simple and elementary many of the fifteen fundamental properties are, in order to fully appreciate, and accept, what is being said. It is not profound, except that we lack the ability to see: the fifteen properties of living structure are easily found, and all over — wherever there is true life! And it is not a matter of projection, as when we often see “faces” when we are looking at a rock or a cloud or the burnt edge of a pancake. These properties are simple and ordinary structural features which are inherent in living structure, and which can be easily spotted and identified, once given a name.

Alternating repetition in the rings of a tree.

Alternating repetition in the ripples of a stream -- strikingly similar to the rings on the tree, in an utterly different context.

It might be more difficult to believe there is any meaningful reason for naming these properties. For example, you might say that repetition is only a logically necessary “quality” of something which exists in the plural, and therefore secondary, and not a true property in its own right. Alexander answers:

But this is not so. In all these cases, the significant issue is the coherence of the secondary centers. The defining feature for alternating repetition lies in the fact that the secondary centers are coherent in their own right, are not left over. This happens in most natural systems because the secondary centers occur as coherent systems in themselves, with their own laws, their own defining processes and stability. […]

In the mackerel cloud formation… [t]he dynamics of vapor formation create clouds of a certain size. The nucleation of the vapor in this clump “sweeps” another volume clean of vapor. The space loses its vapor as the denser droplets form in the adjacent zone. As the cloud forms, the space full of vapor and the spaces emptied of vapor alternate and form the striated pattern we see in the sky. (NOPL, 259-60)

Mackerel Sky

In addition, as this last example suggests, the creation of any particular alternating repetition will be governed by the larger wholeness which is shaping it, and which it, in turn, enhances. The wholeness of a structure can be profoundly shaped by the presence of alternating repetition. We know this already, even as children. Hardly anything is as instinctive in the development or an ornamental pattern, for instance, than to insert a form of alternating repetition.

A drawing while waiting, by a young girl at our door (several weeks ago... we never clean our windows!) revealing alternating repetition between the lines and the wedges, added (probably almost unconsciously) to enhance the life of the circle.

That does not mean it is easy. As has been mentioned (in an earlier post), the apparent presence of the “rule” does not define or produce “living structure.” Instead, living structure will consistently be found to consist of these certain properties. When we try to simply “follow the rules” we produce mechanical and dead repetition. The properties function as enhancers and intensifiers of a latent or already living whole, and without sensitivity to this whole — without being able to “feel” it, deeply — any additions will only serve to undercut the life that is present.

Alternating repetition in the beautiful and disciplined strokes of a rower in the Seattle Ship Canal.

~*~***~*~

A photo of light:

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