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.
Haeckel seemed to have some inkling of this: his description of Aulonia hexagona does mention that there are a few pentagonal, and indeed square, facets in the radiolarian’s shell. *Ironically, it was Challenger’s chemist, John Young Buchanan, who debunked Haeckel’s Bathybius protoplasm. LESSONS OF THE BEEHIVE j 49 Fig. 2.9: The Atlas of Ernst Haeckel presents a vast array of beautiful radiolarian exoskeletons. The number of pentagons needed to bend a sheet of hexagons into a closed shell is
other two.’ Thus, Pappus concluded, the bees are possessed with ‘a certain geometrical forethought’. Pappus does not make himself terribly clear, however, for if you want a cell to hold more honey then you can simply make it bigger, whether it is hexagonal, square or indeed star-shaped. The eighteenth-century French scientist Rene´ de Re´aumur made a more thorough statement of the problem, pointing out that what matters is not the volume of the cavities but the area of the walls: to ﬁll a given
considered as mere shapes—and yet we don’t hesitate to see them as examples of living morphology. Why? Perhaps we sense a kind of purpose, of design, in these forms? They are ‘complex’, certainly, but what does that mean? They may have some regularity or symmetry—the bilateral symmetry of the animals, the repeated branching of the tree—but that can’t be all there is to it, for surely it is often in a high degree of regularity and symmetry, in the onset of crystallinity, that we might imagine we
are biological advantages to these patterned mineral trellises. They offer robust protection at a low cost in materials and weight. Their open, porous structure leaves room for organic ﬁbres and tissues to thread through, just as cells and blood vessels pass through the mineral fabric of bone. And there are more exotic beneﬁts to the periodic patterning too. As we saw for butterﬂy wings, it can supply a kind of lattice for scattering light and creating colour. But orderly microscopic 96 j
3: Making Waves Stripes in a Test Tube 103 4: Written on the Body Hiding, Warning, and Mimicking 151 5: Rhythms of the Wild Crystal Communities 200 6: How Does Your Garden Grow? The Mathematics of a Daisy 226 7: Unfolding the Embryo The Formation of Body Plans 257 Appendices 287 Bibliography 295 Index 303 This page intentionally left blank Preface and acknowledgements A my 1999 book The Self-Made Tapestry: Pattern Formation in Nature went out of print, I’d often be contacted