Shapes: Nature's Patterns: A Tapestry in Three Parts
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Patterns are everywhere in nature - in the ranks of clouds in the sky, the stripes of an angelfish, the arrangement of petals in flowers. Where does this order and regularity come from? It creates itself. The patterns we see come from self-organization. Whether living or non-living, scientists have found that there is a pattern-forming tendency inherent in the basic structure and processes of nature, so that from a few simple themes, and the repetition of simple rules, endless beautiful variations can arise.
Part of a trilogy of books exploring the science of patterns in nature, acclaimed science writer Philip Ball here looks at how shapes form. From soap bubbles to honeycombs, delicate shell patterns, and even the developing body parts of a complex animal like ourselves, he uncovers patterns in growth and form in all corners of the natural world, explains how these patterns are self-made, and why similar shapes and structures may be found in very different settings, orchestrated by nothing more than simple physical forces. This book will make you look at the world with fresh eyes, seeing order and form even in the places you'd least expect.
deﬁned, and can be seen to be a consequence of a simple growth law. Thompson admitted that in general it was no easy thing to ﬁnd mathematical expressions that describe the organic forms of nature, and on the whole he was right. But as this example illustrates, that is not really the right way to proceed. Equations describing the surfaces of the shells in Fig. 1.15b would indeed be cumbersome, and probably not very illuminating. It is far more instructive to look for the algorithm that generates
basic repeating unit is one with the symmetry properties of a cube. Here the pores form in all three dimensions, creating not distinct layers connected by channels but instead a labyrinthine network—in fact, two interpenetrating networks—laced through all of space. The key to the formation of periodic minimal surfaces by surfactants is that, with the surface area of the bilayers ﬁxed by how much surfactant there is in the solution, these surfaces provide the best way to pack that surface into the
available volume: there are no highly bent regions, since the mean curvature is zero everywhere. Luzzati wondered whether, given that cell membranes are so similar to surfactant bilayers, structures like these might be found in living cells, where they might perhaps provide complex plumbing systems. Indeed, the tangle of membrane channels and pores in our cells known as the smooth endoplasmic reticulum, where lipids and some proteins are manufactured, looks very much like the disordered sponge
go round? To answer this we must go instead to the mechanical engineer, who explains how they are connected to the engine via a crankshaft . . . and before long you are getting into an account of the mechanics of the internal combustion engine. So what, we might ask, are the mechanics that create biological form? The standard answer, from what D’Arcy Thompson might have called the adaptionists, is that we must reason a posteriori, seeking to understand what we observe in terms of its functional
be the identiﬁcation of a genuine morphogen—a chemical compound that diffuses through the tissues, switching on pigmenting genes as it goes. So far, nothing of that kind has been identiﬁed for animal marking patterns. But we will see in the ﬁnal chapter that there is now good evidence for diffusing morphogens of a more general sort that control development and growth in embryos. On the wing Since Liesegang bands were the closest D’Arcy Thompson came to ﬁnding a reaction–diffusion system, we can