11. Patterns in Nature (part two)

I’d like to return now to talking about patterns in nature. Besides the Golden Section, branching patterns have fascinated me for a long time and I’ve always wondered if there are common characteristics among the many different branching patterns in nature. Besides plants, you see similar patterns in river systems, human blood vessels, bacterial colonies, and even electricity (lightning). Why are branching patterns so common?

Based on what I've read, the short answer is that a branching pattern is a very efficient way to distribute or collect something from a large area. A river system collects all the rain water that falls in a watershed and brings it together to flow to the sea. A tree distributes leaves out in a three-dimensional shape to collect as much sunlight as possible, while also dispersing nourishment collected from the soil. Blood vessels are moving blood around the body to distribute oxygen and nutrients. Since all these systems are made to do the same basic thing, is their structure based on similar principles?

Similarity of Branching Patterns

Certainly you can see some visual similarities between the patterns of a tree branching and that of a river system. Scientists from different disciplines have studied this in depth and think there are similarities, for example the hydrologist Luna Leopold has said that, “there appears to be an inherent economy in the structure of a branch network.”

An idea called the “principle of least work” has been put forth to explain one aspect of the similar branching structures in different systems. The concept is that branches develop in a way to minimize the energy used to keep fluids circulating. Where a branch occurs is said to be determined by to the ratio of the size of the trunk to the branch. If the branch is small relative to the trunk, then it is more efficient to keep the fluid in the larger artery as long as possible, so the branch would tend to be higher up and closer to a 90 degree angle. If the branch and trunk are closer to the same diameter then it would tend to be lower down and closer to a zero degree angle. This is essentially because the larger diameter means less friction per unit. (There is much more detail on the math and graphic studies behind this starting with the Resources listed below.)

This makes sense at an abstract level, but in nature we don’t see several trees in a row with exactly identical branch structures. There are many other factors that can influence the growth of each branch – sunlight, temperature, available energy and raw materials, proximity to other branches. Its easy to personify a tree and think of it as consciously putting out its branches to maximize efficiency, but in fact it is an ongoing trial and error process with the less successful branches withering and dying off.

Comparing tree branching to a river system, there are obvious differences, related of course to the physics of the space they inhabit – trees grow up against gravity to reach the sunlight, while rivers go downhill with gravity. Leaf veins branch out to distribute fluids but also divide the surface up into smaller cellular units and provide structure. Vascular systems exist within cellular masses with other forces acting on them. So, it seems like the the simple answer is that yes, there are conceptual patterns that underlie branching structures, but not to the point that you see precise similarities.

Branching Patterns and Landscape Design

Part of what I think is fascinating and inspiring about natural patterns is the infinite variety within an understandable general structure. Human built things tend to have much less variety, mainly because of the efficiencies of parts that are mass produced and standardized. It seems to me that branching patterns have the potential to add visual appeal to designed spaces in a lot of different ways. A building’s structure, the collection of a site’s rainwater, or the path system that brings people from their cars to the front door could all use branching structures. Let’s explore one possibility - the planning of neighborhoods - why do our cities tend to use grid-like patterns instead of branching ones?

One of the typical functions of a city’s roads is to distribute people from a central work and shopping area out to individual homes. The well-known architect Christopher Alexander famously said “A City is Not A Tree” but I had to see for myself. I drew a plan of a hypothetical neighborhood using a branching pattern, and even though it looks nice on paper, I realized that there really are efficiencies in a grid that aren’t equaled in a branching system. Most natural branching patterns flow in only one way, so when you are dealing with car traffic, the acute angle of a tree branch is not nearly as good as a 90 degree intersection for moving in any direction. Branches also naturally concentrate flow the further downstream you get, which in terms of roads means traffic jams. I had to add a bike and pedestrian trail network to connect between the branches for travel horizontally within the neighborhood; otherwise it’s a long walk to your friend’s house on another branch. So the branching pattern isn’t the best one for all situations, although I think this could be studied more.

Overall we see that branching type patterns are very common in nature, but their specifics vary greatly according to purpose, context and other environmental factors. They generally occur when there is a large area to distribute or collect resources from, utilizing smaller and smaller branches as they reach out to the periphery of the area. Ultimately these branching patterns often become fractal in nature – having similar pattern units repeated over and over at smaller and smaller scales. This is how I visualize root systems – you may not actually see roots in the soil when you dig, but there are very thin little tendrils woven in there, maximizing the ability of the plant to absorb water and minerals. Branching patterns are so common in nature that we use them as a conceptual guide for all kinds of thinking, from family trees, to computer directory trees. Maybe one day we will even be able to grow a building in the same way a tree grows its branches out!

References:

Patterns in Nature, by Peter S. Stevens

On Growth and Form, by D’Arcy Thompson

Trees and Streams: The Efficiency of Branching Patterns, by Luna Leopold

A City is Not A Tree, by Christopher Alexander

Branches, by Philip Ball  (this is part of a great series of recent books that I'm just getting into - looking like the best, most current resource on this topic, so I may be updating things later!)