Branches: Nature's Patterns: A Tapestry in Three Parts
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As part of a trilogy of books exploring the science of patterns in nature, acclaimed science writer Philip Ball here looks at the form and growth of branching networks in the natural world, and what we can learn from them.
Many patterns in nature show a branching form - trees, river deltas, blood vessels, lightning, the cracks that form in the glazing of pots. These networks share a peculiar geometry, finding a compromise between disorder and determinism, though some, like the hexagonal snowflake or the stones of the Devil's Causeway fall into a rigidly ordered structure. Branching networks are found at every level in biology - from the single cell to the ecosystem. Human-made networks too can come to share the same features, and if they don't, then it might be profitable to make them do so: nature's patterns tend to arise from economical solutions.
three-dimensional world, in which objects have ‘bulk’—they have a volume, enclosed by surfaces. There are objects in the world that are to all intents one- and two-dimensional too. Laid out straight, a piece of string is one-dimensional: you could say that it has ‘length’ but no ‘width’ or ‘height’. Of course, it does have width and height, but these are negligible in comparison to the length. The piece of string is strictly speaking a three-dimensional object in which two of the dimensions are
The thinner they get, the fewer flaws there are. So cracks have nowhere to start from. In analogous fashion, Galileo (who was very interested in discovering why things break) found that the shipbuilders of Venice paid more attention to the construction of big ships than small ones—because, they told him, big ships break more easily. There are simply more places on a big ship where a crack might start. But why, once a crack is initiated by a tiny imperfection, does it then grow with such awesome
shape of the hills and valleys are assigned by a random-number generator, the result is a topography that is certainly uneven but looks wrong. Fractal landscapes are ‘noisy’ and unpredictable, but there is more to them than chance alone. Fig. 4.11: A vertical slice through a rugged valley reveals an irregular profile of peaks and valleys (a). A horizontal cut, meanwhile, isolates islands—contour lines corresponding to cross-sections of the peaks, separated by gaps (b). Fig. 4.12: Self-affine
even for rather severe amounts of link failure. This central cluster merely sheds little ‘islands’ of nodes as the damage gets worse (Fig. 6.6b). The network doesn’t shatter, but gently deflates. Since breakdowns do happen—servers get jammed or malfunction—this is surely just the kind of property one would like in a network like the Internet. But no one designed it that way. Indeed, if they had designed it, they probably would have chosen some other network topology that was nothing like as
networks 151–175 Stanley, Gene 22, 23, 66 Stark, Colin 109 Strahler, Arthur 103 stream networks, see river networks street patterns 93–95 see also road networks stress concentration, in fracture 77, 78 Strogatz, Steven 156–159, 161, 167 surface tension 18, 47, 182 symmetry-breaking 184, 185, 190, 196, 197 T’ang Chin 2 Taylor, Geoffrey 46, 181, 193, 194 tearing 81 thermodynamics 185, 189–193 non-equilibrium 185–189, 207–210 Thompson, D’Arcy Wentworth 13, 14, 20, 71, 74, 76, 142,