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.
growth is accompanied by a sharpening and narrowing of the tip, generating a tendril that itself sprouts random appendages through the same growth instability. Notice that the random, diffusive motion of the particles is essential to all of this. If they were instead all propelled towards the cluster along straight trajectories, like rain falling on a road, the edge of the cluster would just advance uniformly. Fig. 2.4: A cluster of aggregated particles grown by the diffusion-limited aggregation
simply travelled around the tube’s axis at a fixed angle, cutting out a perfect helix (Fig. 3.4f ). Such helical cracks are rumoured (this is not easy to check) to be found in frozen natural gas pipelines in Alaska, sometimes winding their way around the pipes for miles. Fig. 3.4: Growth instabilities in slowly propagating cracks through a glass plate. The crack is initiated at a notch, and advances owing to the stresses produced as the hot plate is lowered into a water bath. If the speed is
must postulate two chemical triggers, whereas in plants only auxin has so far been identified as one such. Steffen Bohn and his colleagues in Paris have recognized a similarity between vascular webs and crack networks in thin layers of brittle material (see page 95). In both cases, for example, branch intersections at right angles are common. They have proposed that, by analogy with cracking, vein networks might be controlled by mechanical forces rather than chemical signals. They point out that
a particular crack speed. In addition, the change in state during an equilibrium phase transition may involve a breaking of symmetry. Crystalline ice has an ordered molecular structure (in fact it has many ordered structures), while liquid water is disorderly at the molecular scale. Again, you could be forgiven for thinking that symmetry is therefore broken during melting, but in fact it is the other way around: symmetry is broken during freezing, because whereas the liquid state is isotropic