Permaculture Designers Manual
CHAPTER 4 – PATTERN UNDERSTANDING
Section 4.15 –
Branching and its Effects in Permaculture
Various sections, plans, and views of our one tree model reveal very different sectional PATTERNS, all of which are inherent and most of which recur in many other natural forms.
Benoit Mandelbrot assembled his own insights, and the speculations of others, to found a mathematics of fractals (his term, from the Latin fractus, or shattered), which is evolving to make sense of irregular phenomena, as Euclid did for more regular and measurable forms (New Scientist, 26 Apr ’84, p.17 and 4 Apr ’85, p.JJ-35).
Fractals are as common in nature as in abstractions, and examples are as diverse as impact shatter-zones, clouds, forked lightning, neuron nets and their signals, computer searching procedures, plant identification keys, snowflakes and tree branches or roots. Some typical fractal forms are illustrated (Figure 4.22).Others make up the complex lengths of coastlines and the intricacies of turbulence.
In our tree form (Figure 4.1), these fractal patterns (as branches and roots) are contained within a form that would be comprehensible to Euclid, having straight axes, a plane, and regular curved lines, which can be drawn as arcs of perfect circles.
Thus the apparent chaos of fractals can be seen to underlie quite regular (but never perfect) shapes in nature as branches underlie the crown canopy of a tree. As Mandelbrot has demonstrated, fractals have their own regular generators and evolutions.
Looking down on a bare winter-deciduous tree, we see a typical fractal, which we can also find in the fulgurites (sand fused by lightning) in sand dunes, and in the shatter zones of explosions.
Tree roots are, in fact, a slow shatter or explosion underground. One way to plant an apple tree in very hard ground is to detonate a small plug of gelignite a foot or two below the surface; the roots will follow the shatter pattern, and further elaborate it.
Scatters of objects may at first seem to present a class of events unrelated to either flow models or fractals, but fractals are being used to describe the scatters of tree clumps in grassland, or lichen on a stone.
In a sense, the surface of spheroids created by branched phenomena (like the plan view of a tree crown) may show such apparently random scatters as growth points; or a curved section through the cut or pruned branches below the crown of a tree would also appear to be a scatter of points (Figure 4.1 E).
These can be measured by fractal analysis.
Fractal theory may give us a way to measure, compute, and design for branched or scattered phenomena, but we also need to understand the physical advantages of developing ever smaller conduits.
Vogel (1981) gives many insights into this process and its effects. Large conduits are of use in mass transport, but both the laminar flow patterns within them and the fact that they have a small surface area relative to their volume makes them inefficient for the diffusion of materials or the conduction of heat across their walls.
Ever smaller conduits have different qualities: now is slow, almost viscous in very small tubes or branches; direction changes in small branches are therefore possible without incurring turbulence or energy losses. Walls can be permeable, and efficient collection, exchange, and transfer is effected (whether of materials or physical properties such as heat and light).
Many small conduits efficiently interpenetrate the exchange media (Figure 4.23).
Wherever there is a need to collect or distribute materials, or to trade both ways with media, branching is an effective response.
In design, therefore, we need to use “many paths” in such situations as home gardens, where we are always trading nutrients as our main activity. There is little advantage in forming these paths as straight lines (speed is not of the essence), but rather in developing a set of cut de sacs or keyhole-shaped beds (this is also the shape of sacs in lungs).
Convoluted paths in gardens have the same effect. They either bring the gardener into better contact with the garden, enabling collection and servicing to occur, or create better mutual exchange between the species in the garden.
The high-pressure/low -flow nature of minor branches demands a very large total cross-sectional area of these in relation to the main supply arteries. Such small conduits may develop areas which in some are 300 – 1,600 times that of the supply artery (our main roads are therefore much less in area than the foot tracks that lead off them).
As an applied strategy, multiple small paths enhance our access to food systems or in fact any system where we both take and give materials.
In organisms, the multiple branches give the being a chance to recover from injury, preserve information and permit re-growth in the event of minor damage.
It is a fool-proof system of interchange.
Another way to affect interchange is to elaborate on the walls of larger conduits by involutions, attached fins, irregular surfaces, or to create spirals in fluids or gases by bending or spiraling the conduits themselves, and in general inducing a larger surface of contact between the material transported and the media with which we wish to exchange nutrients, heal, or gases.
Branching in trees is as often a result of external forces (wind and salt pruning, secateurs or insect attack) as it is a result of internal cell patterns; it is as much forced upon things as it is the “best thing to do.”
We must therefore see the branched form as an interaction between an organism or process, the purpose it serves, and the external forces of the media in which the organism is immersed (the forces acting on it externally to deform the perfect pattern).
Along the streamlines (S1-S9 of our model Figure 4.1), fluids and gases may pass in conduits or along “transmission cords“, food and signals are relayed to cells, and gases exchanged.
Organs served by or serving these systems are half-models of our tree (kidneys, lungs) or branching fractals (mesenteries).
No matter how long or complex conduits are, in the end their contents diverge, escape and disperse, and at the intake materials are gathered from dispersed sources.
It is this gathering and dispersal from both ends and margins of events that is a basic function of the tree-like forms that pervade living natural systems and such phenomena as rivers or lava flows.