Branches: Nature's Patterns: A Tapestry in Three Parts by Philip Ball

By Philip Ball

As a part of a trilogy of books exploring the technological know-how of styles in nature, acclaimed technology author Philip Ball the following seems to be on the shape and development of branching networks within the flora and fauna, and what we will be able to examine from them.

Many styles in nature convey a branching shape - timber, river deltas, blood vessels, lightning, the cracks that shape within the glazing of pots. those networks proportion a weird geometry, discovering a compromise among disease and determinism, even though a few, just like the hexagonal snowflake or the stones of the Devil's Causeway fall right into a rigidly ordered constitution. Branching networks are came upon at each point in biology - from the only telephone to the atmosphere. Human-made networks can also come to proportion a similar gains, and in the event that they don't, then it would be ecocnomic to cause them to achieve this: nature's styles are inclined to come up from budget friendly options.

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24 j NATURE’S PATTERNS: BRANCHES Fig. 15: The six branches of some snowflakes can be quite different from one another in their fine details, even though at a glance they look symmetrical (a). Such flakes can be grown in a computer model of aggregating particles that assigns at random where a new particle gets attached, subject to the constraint that the particle positions must lie on a hexagonal grid (b). There is nothing in the rules of the model to ensure that all branches are the same, and indeed they are not the same; but our eyes are fooled into seeing more symmetry than there really is by the uniformity of the branching angles.

We are used to living in a 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 TENUOUS MONSTERS j 37 two of the dimensions are reduced to almost nothing; if the string were infinitely thin, it would be truly one-dimensional.

One aspect of the self-similarity of the Mandelbrot set is that, as you zoom in on any region of the perimeter, the ominous black bulb keeps reappearing like a malformed Russian doll. Because of scale invariance, fractal forms have no boundary. There are points in the plane of the Mandelbrot set that are unambiguously inside or outside the black region, but if you are right on the ‘edge’ then you cannot be sure which side you’re on: each time you zoom in further, you see more of the convolutions.

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