Patterns: Branches

‘Y’ – The perfect letter. The wishbone, cure the fork in the road. The empty wineglass, discount the question we ask over and over again. – anonymous

One of the most “natural” effects that we can create under laboratory conditions is brownian motion.  Botanist Robert Brown once noted that through a microscope the magnified particles of pollen in water appeared to move randomly, but with no apparent explanation why.  Later, Albert Einstein investigated brownian motion and deduced that the particles were jostled by individual water molecules in an excited state – much like a giant weather balloon bouncing around on top of a crowd of people.

By carefully mapping the movement of these particles, Einstein not only found evidence for the existence of molecules, but discovered their size and calculated their density at specific pressures and temperatures.

Brownian motion can also be observed in particles that aggregate into clusters – and when left to do so, they create delicate branching figures called diffusion-limited aggregates, or Lichtenberg figures. These can be created slowly, by allowing copper sulphate to flow naturally in an electrified field, or quickly, by prompting lightning to strike a plexiglass block or a patch of sandy desert.

These same figures can be found in countless examples of ecology, hydrology, cartography and economy. Any time you find an evolved mechanism that transports large volumes of material, you should find branching patterns.

The wooden trunk of a tree provides the strength that keeps the tree upright in the wind, but it also provides another critical function – it carries the water required for the leaves to perform photosynthesis.  A mature oak in summer may draw fifty gallons a day up its trunk and release it through leaf transpiration.

There is no active pump in a tree.  Evaporation in the stoma of the leaf – thousands per leaf and billions per tree – creates a massive collective force of vacuum, drawing water is up from the earth through the roots and sapwood by negative pressure.  The wood and inner bark of a tree form an amazing network of water paths, delivering just enough water to every growing bud and leaf of the tree. The water provided by that network is the necessary solvent which enables the tree to convert sunlight and carbon dioxide into sugar, which fuels its growth, and oxygen, a byproduct we find useful. By burning that sugar, it deposits carbon within itself and so over centuries, a tree creates itself from a hundred tons of solidified air.

From the single trunk at its base to the leaf buds at the tip of the twigs of its outermost crown, a tree is all branches.

The form of a healthy deciduous tree in winter – the branches of a live oak for instance, follow this model beautifully, as do it’s roots, in a similar structure. An oak’s shape can be detected easily to anyone who is familiar – but what elements of it are so easy to pick out?

The oak’s plump and stout appearance is obvious in comparison to a maple, beech or willow. These forms, as complex as they are, are dictated by just a few simple decisions the tree’s DNA makes when creating a new branch:  The ratio of thickness to length of the current branch (A) before creating a new branch (B), the ratio of A’s thickness to B’s thickness, the angle at which B exits A, and whether to create several branches simultaneously (opposite) or one following another (alternating).

By manipulating these parameters, we can create trees in computer simulation that very much appear to be maples, or oaks or tamaracks.  These same branching rules, with influence from our skeletal system, create the shape of the blood vessels in our body.  Different sets of the same branching settings can model our very different looking nervous system.

This same set of controls can be used to simulate (or analyze) rivers, highways, the paths ants take through the jungle while scavenging for food, or the paths that armies take marching to battle.

One interesting feature they all seem to exhibit is one of order:  Physical features can only be so large – the widest river on Earth is the Amazon, about 6 km (3.75 mi) in width.  Every tributary formed is about 1/5 the size of the main body, which means a second order branch is about 1.2 km (.75 mi) and the sixth order is less than a meter (about 3 feet).  The seventh would be smaller than your hand, and the eighth smaller than your thumb.

In general, naturally branching systems – like brownian trees, rivers and the nervous system – don’t go deeper than six levels of order before giving in to collapse and turbulence.  This makes sense – as blood vessels divide they get smaller. If they get too small, then platelets simply can’t travel in them.  As rivers get smaller, the friction of water against the banks overcomes the downward flow of water, causing pools and ponds.  As tree branches get smaller, new leaves crowd out the old and without sun both photosynthesis and the vacuum-powered pump system breaks down.  As columns of soldiers get too thin, they are easily overcome by the enemy.

Hardly any design will scale infinitely – most won’t survive a single order of magnitude.  A deeply branching system can rapidly be overcome by it’s own Infrastructure needs and limitations of scale.

This phenomenon occurs in organizational hierarchies. The deeper an org chart, the slower information disseminates from the most distal nodes, and the more information loss it suffers.  Like the children’s game telephone, the boss saying he likes the blue shirt his wife bought him may become a corporate mandate for Pantone 643U by the time it makes it five layers down the chain to the designers in marketing.  A vendor being unable to provide 643U in sufficient quantity may cause a deliverable to slip and the company may miss it’s third quarter estimates because of bad communication.

This example seems ridiculous and contrived, and it is. It’s also the sort of thing that happens on a regular basis.

If the Amazon, beginning miles of water wide, can’t drive an inch of water after 7 orders of branching, how many branches do you think the depth of a CEO’s values and vision can penetrate into an organization?

Hierarchy and branching are valuable tools in our designs.  They allow us to route material, energy, and information from a central source to remote points in a rapid and efficient fashion – up to the limits of its design and the level of resources available. Keep your eyes open and you’ll probably see branching systems all around you.


Scott is a multidiscipline technologist and problem wrangler. His day jobs include writing code for mid-size businesses and startups, consulting on business process for young companies and organizations, and applying permaculture design philosophy wherever it’s appropriate.

Scott is available for limited consultation on a myriad of topics. [email protected]

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